Derivatives Project Report

Derivatives – Indian Scenario - 1 -

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1.0 Introduction to derivativesThe emergence of the market for derivative products, most notably forwards, futures and

options, can be traced back to the willingness of risk-averse economic agents to guard

themselves against uncertainties arising out of fluctuations in asset prices. By their very

nature, the financial markets are marked by a very high degree of volatility. Through the

use of derivative products, it is possible to partially or fully transfer price risks by

locking-in asset prices. As instruments of risk management, these generally do not

influence the fluctuations in the underlying asset prices. However, by locking-in asset

prices, derivative products minimize the impact of fluctuations in asset prices on the

profitability and cash flow situation of risk-averse investors.

Derivative products initially emerged, as hedging devices against fluctuations in

commodity prices and commodity-linked derivatives remained the sole form of such

products for almost three hundred years. The financial derivatives came into spotlight in

post-1970 period due to growing instability in the financial markets. However, since their

emergence, these products have become very popular and by 1990s, they accounted for

about two-thirds of total transactions in derivative products. In recent years, the market

for financial derivatives has grown tremendously both in terms of variety of instruments

available, their complexity and also turnover. In the class of equity derivatives, futures

and options on stock indices have gained more popularity than on individual stocks,

especially among institutional investors, who are major users of index-linked derivatives.

Even small investors find these useful due to high correlation of the popular indices with

various portfolios and ease of use. The lower costs associated with index derivatives vis-

vis derivative products based on individual securities is another reason for their growing

use.


The following factors have been driving the growth of financial derivatives:

1. Increased volatility in asset prices in financial markets,

2. Increased integration of national financial markets with the international markets,

3. Marked improvement in communication facilities and sharp decline in their costs,

4. Development of more sophisticated risk management tools, providing economic

agents a wider choice of risk management strategies, and

5. Innovations in the derivatives markets, which optimally combine the risks and

returns over a large number of financial assets, leading to higher returns, reduced

risk as well as trans-actions costs as compared to individual financial assets.

1.1 Derivatives defined

Derivative is a product whose value is derived from the value of one or more basic

variables, called bases (underlying asset, index, or reference rate), in a contractual

manner. The underlying asset can be equity, forex, commodity or any other asset. For

example, wheat farmers may wish to sell their harvest at a future date to eliminate the

risk of a change in prices by that date. Such a transaction is an example of a derivative.

The price of this derivative is driven by the spot price of wheat which is the “underlying”.

In the Indian context the Securities Contracts (Regulation) Act, 1956 (SC(R) A) defines

“equity derivative” to include –

1. A security derived from a debt instrument, share, loan whether secured or

unsecured, risk instrument or contract for differences or any other form of

security.

2. A contract, which derives its value from the prices, or index of prices, of

underlying securities.

The derivatives are securities under the SC(R) A and hence the trading of derivatives is

governed by the regulatory framework under the SC(R) A.1

1.2 Types of derivatives

The most commonly used derivatives contracts are forwards, futures and options which

we shall discuss in detail later. Here we take a brief look at various derivatives contracts

that have come to be used.

1 Source: www.nse-india.com


Forwards: A forward contract is a customized contract between two entities, where

settlement takes place on a specific date in the future at today’s pre-agreed price.

Futures: A futures contract is an agreement between two parties to buy or sell an asset at

a certain time in the future at a certain price. Futures contracts are special types of

forward contracts in the sense that the former are standardized exchange-traded contracts.

Options: Options are of two types - calls and puts. Calls give the buyer the right but not

the obligation to buy a given quantity of the underlying asset, at a given price on or

before a given future date. Puts give the buyer the right, but not the obligation to sell a

given quantity of the underlying asset at a given price on or before a given date.

Swaps: Swaps are private agreements between two parties to exchange cash flows in the

future according to a prearranged formula. They can be regarded as portfolios of forward

contracts. The two commonly used swaps are:

Interest rate swaps: These entail swapping only the interest related cash flows

between the parties in the same currency.

Currency swaps: These entail swapping both principal and interest between the

parties, with the cash flows in one direction being in a different currency than

those in the opposite direction.

Warrants: Options generally have lives of upto one year, the majority of options traded

on options exchanges having a maximum maturity of nine months. Longer-dated options

are called warrants and are generally traded over-the-counter.

LEAPS: The acronym LEAPS means Long-Term Equity Anticipation Securities. These

are options having a maturity of upto three years.

Baskets: Basket options are options on portfolios of underlying assets. The underlying

asset is usually a moving average or a basket of assets. Equity index options are a form of

basket options.


Swaptions: Swaptions are options to buy or sell a swap that will become operative at the

expiry of the options. Thus a swaption is an option on a forward swap. Rather than have

calls and puts, the swaptions market has receiver swaptions and payer swaptions. A

receiver swaption is an option to receive fixed and pay floating. A payer swaption is an

option to pay fixed and receive floating.2

1.3 Participants and Functions

Three broad categories of participants - hedgers, speculators, and arbitrageurs - trade in

the derivatives market. Hedgers face risk associated with the price of an asset. They use

futures or options markets to reduce or eliminate this risk. Speculators wish to bet on

future movements in the price of an asset. Futures and options contracts can give them an

extra leverage; that is, they can increase both the potential gains and potential losses in a

speculative venture. Arbitrageurs are in business to take advantage of a discrepancy

between prices in two different markets. If, for example, they see the futures price of an

asset getting out of line with the cash price, they will take offsetting positions in the two

markets to lock in a profit.

The derivative market performs a number of economic functions. First, prices in an

organized derivatives market reflect the perception of market participants about the future

and lead the prices of underlying to the perceived future level. The prices of derivatives

converge with the prices of the underlying at the expiration of derivative contract. Thus

derivatives help in discovery of future as well as current prices. Second, the derivatives

market helps to transfer risks from those who have them but may not like them to those

who have appetite for them. Third, derivatives, due to their inherent nature, are linked to

the underlying cash markets. With the introduction of derivatives, the underlying market

witnesses higher trading volumes because of participation by more players who would

not otherwise participate for lack of an arrangement to transfer risk. Fourth, speculative

trades shift to a more controlled environment of derivatives market. In the absence of an

organized derivatives market, speculators trade in the underlying cash markets.

Margining, monitoring and surveillance of the activities of various participants become

2 Source: Options Futures & Other Derivatives John C Hull


extremely difficult in these kind of mixed markets. Fifth, an important incidental benefit

that flows from derivatives trading is that it acts as a catalyst for new entrepreneurial

activity. The derivatives have a history of attracting many bright, creative, well-educated

people with an entrepreneurial attitude. They often energize others to create new

businesses, new products and new employment opportunities, the benefit of which are

immense. Sixth, derivatives markets help increase savings and investment in the long run.

Transfer of risk enables market participants to expand their volume of activity.

Derivatives thus promote economic development to the extent the later depends on the

rate of savings and investment.

1.4 Development of exchange-traded derivatives

Derivatives have probably been around for as long as people have been trading with one

another. Forward contracting dates back at least to the 12th century, and may well have

been around before then. Merchants entered into contracts with one another for future

delivery of specified amount of commodities at specified price. A primary motivation for

prearranging a buyer or seller for a stock of commodities in early forward contracts was

to lessen the possibility that large swings would inhibit marketing the commodity after a

harvest.

Although early forward contracts in the US addressed merchants’ concerns about

ensuring that there were buyers and sellers for commodities, “credit risk” remained a

serious problem. To deal with this problem, a group of Chicago businessmen formed the

Chicago Board of Trade (CBOT) in 1848. The primary intention of the CBOT was to

provide a centralized location known in advance for buyers and sellers to negotiate

forward contracts. In 1865, the CBOT went one step further and listed the first “exchange

traded” derivatives contract in the US; these contracts were called “futures contracts”. In

1919, Chicago Butter and Egg Board, a spin-off of CBOT, was reorganized to allow

futures trading. Its name was changed to Chicago Mercantile Exchange (CME). The

CBOT and the CME remain the two largest organized futures exchanges, indeed the two

largest “financial” exchanges of any kind in the world today.


The first stock index futures contract was traded at Kansas City Board of Trade.

Currently the most popular index futures contract in the world is based on S&P 500

index, traded on Chicago Mercantile Exchange. During the mid eighties, financial futures

became the most active derivative instruments generating volumes many times more than

the commodity futures. Index futures, futures on T-bills and Euro-Dollar futures are the

three most popular futures contracts traded today. Other popular international exchanges

that trade derivatives are LIFFE in England, DTB in Germany, SGX in Singapore, TIFFE

in Japan, MATIF in France, etc.3

Table 1.1 The global derivatives industry: Outstanding contracts, (in $ billion)

1995 1996 1997 1998 1999Exchange traded instruments 9283 10018 12403 13932 13522 Interest rate futures and options 8618 9257 11221 12643 11669 Currency futures and options 154 171 161 81 59 Stock Index futures and options 511 591 1021 1208 1793Some OTC instruments 17713 25453 29035 80317 88201 Interest rate swaps and options 16515 23894 27211 44259 53316 Currency swaps and options 1197 1560 1824 5948 4751 Other instruments - - - 30110 30134

Total 26996 35471 41438 94249 101723

Table 1.2 Chronology of instruments1874 Commodity futures

1972 Foreign currency futures

1973 Equity options

1975 Treasury bond futures

1981 Currency swaps

1982 Interest rate swaps, T note futures, Eurodollar futures, Equity index futures,

Options on T bond futures, Exchange listed currency options

1983 Options on equity index, Options on T-note futures, Options on currency futures,

Options on equity index futures, interest rate caps and floors

1985 Eurodollar options, Swap options

1987 OTC compound options, OTC average options

1989 Futures on interest rate swaps, Quanto options

3 Source: Derivatives in India FAQ Ajay Shah & Susan Thomas


1990 Equity index swaps

1991 Differential swaps

1993 Captions, exchange listed FLEX options

1994 Credit default options

1.5 Exchange-traded vs. OTC derivatives markets

The OTC derivatives markets have witnessed rather sharp growth over the last few years,

which has accompanied the modernization of commercial and investment banking and

globalisation of financial activities. The recent developments in information technology

have contributed to a great extent to these developments. While both exchange-traded

and OTC derivative contracts offer many benefits, the former have rigid structures

compared to the latter. It has been widely discussed that the highly leveraged institutions

and their OTC derivative positions were the main cause of turbulence in financial

markets in 1998. These episodes of turbulence revealed the risks posed to market stability

originating in features of OTC derivative instruments and markets.

The OTC derivatives markets have the following features compared to exchange-traded

derivatives:

1. The management of counter-party (credit) risk is decentralized and located within

individual institutions,

2. There are no formal centralized limits on individual positions, leverage, or

margining,

3. There are no formal rules for risk and burden-sharing,

4. There are no formal rules or mechanisms for ensuring market stability and

integrity, and for safeguarding the collective interests of market participants, and

5. The OTC contracts are generally not regulated by a regulatory authority and the

exchange’s self-regulatory organization, although they are affected indirectly by

national legal systems, banking supervision and market surveillance.


Some of the features of OTC derivatives markets embody risks to financial market

stability.

The following features of OTC derivatives markets can give rise to instability in

institutions, markets, and the international financial system: (i) the dynamic nature of

gross credit exposures; (ii) information asymmetries; (iii) the effects of OTC derivative

activities on available aggregate credit; (iv) the high concentration of OTC derivative

activities in major institutions; and (v) the central role of OTC derivatives markets in the

global financial system. Instability arises when shocks, such as counter-party credit

events and sharp movements in asset prices that underlie derivative contracts, occur

which significantly alter the perceptions of current and potential future credit exposures.

When asset prices change rapidly, the size and configuration of counter-party exposures

can become unsustainably large and provoke a rapid unwinding of positions.

There has been some progress in addressing these risks and perceptions. However, the

progress has been limited in implementing reforms in risk management, including

counter-party, liquidity and operational risks, and OTC derivatives markets continue to

pose a threat to international financial stability. The problem is more acute as heavy

reliance on OTC derivatives creates the possibility of systemic financial events, which

fall outside the more formal clearing house structures. Moreover, those who provide OTC

derivative products, hedge their risks through the use of exchange traded derivatives. In

view of the inherent risks associated with OTC derivatives, and their dependence on

exchange traded derivatives, Indian law considers them illegal.


2.0 Indian Derivatives MarketStarting from a controlled economy, India has moved towards a world where prices

fluctuate every day. The introduction of risk management instruments in India gained

momentum in the last few years due to liberalisation process and Reserve Bank of India’s

(RBI) efforts in creating currency forward market. Derivatives are an integral part of

liberalisation process to manage risk. NSE gauging the market requirements initiated the

process of setting up derivative markets in India. In July 1999, derivatives trading

commenced in India

Table 2.1 Chronology of instruments1991 Liberalisation process initiated

14 December 1995 NSE asked SEBI for permission to trade index futures.

18 November 1996 SEBI setup L.C.Gupta Committee to draft a policy framework for

index futures.

11 May 1998 L.C.Gupta Committee submitted report.

7 July 1999 RBI gave permission for OTC forward rate agreements (FRAs) and

interest rate swaps.

24 May 2000 SIMEX chose Nifty for trading futures and options on an Indian

index.

25 May 2000 SEBI gave permission to NSE and BSE to do index futures trading.

9 June 2000 Trading of BSE Sensex futures commenced at BSE.

12 June 2000 Trading of Nifty futures commenced at NSE.

25 September 2000 Nifty futures trading commenced at SGX.

2 June 2001 Individual Stock Options & Derivatives

2.1 Need for derivatives in India today

In less than three decades of their coming into vogue, derivatives markets have become

the most important markets in the world. Today, derivatives have become part and parcel

of the day-to-day life for ordinary people in major part of the world.

Until the advent of NSE, the Indian capital market had no access to the latest trading


methods and was using traditional out-dated methods of trading. There was a huge gap

between the investors’ aspirations of the markets and the available means of trading. The

opening of Indian economy has precipitated the process of integration of India’s financial

markets with the international financial markets. Introduction of risk management

instruments in India has gained momentum in last few years thanks to Reserve Bank of

India’s efforts in allowing forward contracts, cross currency options etc. which have

developed into a very large market.

2.2 Myths and realities about derivatives

In less than three decades of their coming into vogue, derivatives markets have become

the most important markets in the world. Financial derivatives came into the spotlight

along with the rise in uncertainty of post-1970, when US announced an end to the Bretton

Woods System of fixed exchange rates leading to introduction of currency derivatives

followed by other innovations including stock index futures. Today, derivatives have

become part and parcel of the day-to-day life for ordinary people in major parts of the

world. While this is true for many countries, there are still apprehensions about the

introduction of derivatives. There are many myths about derivatives but the realities that

are different especially for Exchange traded derivatives, which are well regulated with all

the safety mechanisms in place.

What are these myths behind derivatives?

Derivatives increase speculation and do not serve any economic purpose

Indian Market is not ready for derivative trading

Disasters prove that derivatives are very risky and highly leveraged

instruments

Derivatives are complex and exotic instruments that Indian investors will find

difficulty in understanding

Is the existing capital market safer than Derivatives?

2.2.1 Derivatives increase speculation and do not serve any economic purpose

While the fact is...


Numerous studies of derivatives activity have led to a broad consensus, both in the

private and public sectors that derivatives provide numerous and substantial benefits to

the users. Derivatives are a low-cost, effective method for users to hedge and manage

their exposures to interest rates, commodity prices, or exchange rates.

The need for derivatives as hedging tool was felt first in the commodities market.

Agricultural futures and options helped farmers and processors hedge against commodity

price risk. After the fallout of Bretton wood agreement, the financial markets in the world

started undergoing radical changes. This period is marked by remarkable innovations in

the financial markets such as introduction of floating rates for the currencies, increased

trading in variety of derivatives instruments, on-line trading in the capital markets, etc.

As the complexity of instruments increased many folds, the accompanying risk factors

grew in gigantic proportions. This situation led to development derivatives as effective

risk management tools for the market participants.

Looking at the equity market, derivatives allow corporations and institutional investors to

effectively manage their portfolios of assets and liabilities through instruments like stock

index futures and options. An equity fund, for example, can reduce its exposure to the

stock market quickly and at a relatively low cost without selling off part of its equity

assets by using stock index futures or index options.

By providing investors and issuers with a wider array of tools for managing risks and

raising capital, derivatives improve the allocation of credit and the sharing of risk in the

global economy, lowering the cost of capital formation and stimulating economic growth.

Now that world markets for trade and finance have become more integrated, derivatives

have strengthened these important linkages between global markets, increasing market

liquidity and efficiency and facilitating the flow of trade and finance.4

2.2.2 Indian Market is not ready for derivative trading


4 Source: www.nse-india .com


Often the argument put forth against derivatives trading is that the Indian capital market

is not ready for derivatives trading. Here, we look into the pre-requisites, which are

needed for the introduction of derivatives and how Indian market fares:

Table 2.2

PRE-REQUISITES INDIAN SCENARIOLarge market Capitalisation India is one of the largest market-capitalised countries in

Asia with a market capitalisation of more than Rs.765000 crores.

High Liquidity in the underlying

The daily average traded volume in Indian capital market today is around 7500 crores. Which means on an average every month 14% of the country’s Market capitalisation gets traded. These are clear indicators of high liquidity in the underlying.

Trade guarantee The first clearing corporation guaranteeing trades has become fully functional from July 1996 in the form of National Securities Clearing Corporation (NSCCL). NSCCL is responsible for guaranteeing all open positions on the National Stock Exchange (NSE) for which it does the clearing.

A Strong Depository National Securities Depositories Limited (NSDL) which started functioning in the year 1997 has revolutionalised the security settlement in our country.

A Good legal guardian In the Institution of SEBI (Securities and Exchange Board of India) today the Indian capital market enjoys a strong, independent, and innovative legal guardian who is helping the market to evolve to a healthier place for trade practices.

2.2.3 Disasters prove that derivatives are very risky and highly leveraged

instruments


Disasters can take place in any system. The 1992 Security scam is a case in point.

Disasters are not necessarily due to dealing in derivatives, but derivatives make


headlines... Here I have tried to explain some of the important issues involved in disasters

related to derivatives. Careful observation will tell us that these disasters have occurred

due to lack of internal controls and/or outright fraud either by the employees or

promoters.

Barings Collapse

1. 233 year old British bank goes bankrupt on 26th February 1995

2. Downfall attributed to a single trader, 28 year old Nicholas Leeson

3. Loss arose due to large exposure to the Japanese futures market

4. Leeson, chief trader for Barings futures in Singapore, takes huge position in index

futures of Nikkei 225

5. Market falls by more than 15% in the first two months of ’95 and Barings suffers

huge losses

6. Bank looses $1.3 billion from derivative trading

7. Loss wipes out the entire equity capital of Barings

The reasons for the collapse:

Leeson was supposed to be arbitraging between Osaka Securities Exchange and

SIMEX -- a risk less strategy, while in truth it was an unhedged position.

Leeson was heading both settlement and trading desk -- at most other banks the

functions are segregated, this helped Leeson to cover his losses -- Leeson was

unsupervised.

Lack of independent risk management unit, again a deviation from prudential norms.

There were no proper internal control mechanisms leading to the discrepancies going

unnoticed – Internal audit report which warned of "excessive concentration of power

in Leeson’s hands" was ignored by the top management.

The conclusion as summarised by Wall Street Journal article

" Bank of England officials said they did not regard the problem in this case as one

peculiar to derivatives. In a case where a trader is taking unauthorised positions, they

said, the real question is the strength of an investment houses’ internal controls and the

external monitoring done by Exchanges and Regulators. "

Metallgesellschaft


1. Metallgesellshaft (MG) -- a hedge that went bad to the tune of $1.3 billion

Germany’s 14th largest industrial group nearly goes bankrupt from losses suffered

through its American subsidiary - MGRM

2. MGRM offered long term contracts to supply 180 million barrels of oil products

to its clients -- commitments were quite large, equivalent to 85 days of Kuwait’s

oil output

3. MGRM created a hedge position for these long term contracts with short term

futures market through rolling hedge --, As there was no viable long term

contracts available

4. Company was exposed to basis risk -- risk of short term oil prices temporarily

deviating from long term prices.

5. In 1993, oil prices crashed, leading to billion dollars of margin call to be met in

cash. The Company was faced with temporary funds crunch.

6. New management team decides to liquidate the remaining contracts, leading to a

loss of 1.3 billion.

7. Liquidation has been criticised, as the losses could have decreased over time.

Auditors’ report claims that the losses were caused by the size of the trading

exposure.

Reasons for the losses:

The transactions carried out by the company were mainly OTC in nature and hence

lacked transparency and risk management system employed by a derivative exchange

Large exposure

Temporary funds crunch

Lack of matching long-term contracts, which necessitated the company to use rolling

short term hedge -- problem arising from the hedging strategy

Basis risk leading to short term loss

2.2.4 Derivatives are complex and exotic instruments that Indian investors will have

difficulty in understanding



Trading in standard derivatives such as forwards, futures and options is already prevalent

in India and has a long history. Reserve Bank of India allows forward trading in Rupee-

Dollar forward contracts, which has become a liquid market. Reserve Bank of India also

allows Cross Currency options trading.

Forward Markets Commission has allowed trading in Commodity Forwards on

Commodities Exchanges, which are, called Futures in international markets.

Commodities futures in India are available in turmeric, black pepper, coffee, Gur

(jaggery), hessian, castor seed oil etc. There are plans to set up commodities futures

exchanges in Soya bean oil as also in Cotton. International markets have also been

allowed (dollar denominated contracts) in certain commodities. Reserve Bank of India

also allows, the users to hedge their portfolios through derivatives exchanges abroad.

Detailed guidelines have been prescribed by the RBI for the purpose of getting approvals

to hedge the user’s exposure in international markets.

Derivatives in commodities markets have a long history. The first commodity futures

exchange was set up in 1875 in Mumbai under the aegis of Bombay Cotton Traders

Association (Dr.A.S.Naik, 1968, Chairman, Forwards Markets Commission, India, 1963-

68). A clearinghouse for clearing and settlement of these trades was set up in 1918. In

oilseeds, a futures market was established in 1900. Wheat futures market began in Hapur

in 1913. Futures market in raw jute was set up in Calcutta in 1912. Bullion futures market

was set up in Mumbai in 1920.

History and existence of markets along with setting up of new markets prove that the

concept of derivatives is not alien to India. In commodity markets, there is no resistance

from the users or market participants to trade in commodity futures or foreign exchange

markets. Government of India has also been facilitating the setting up and operations of

these markets in India by providing approvals and defining appropriate regulatory

frameworks for their operations.


Approval for new exchanges in last six months by the Government of India also indicates

that Government of India does not consider this type of trading to be harmful albeit

within proper regulatory framework.

This amply proves that the concept of options and futures has been well ingrained in the

Indian equities market for a long time and is not alien as it is made out to be. Even today,

complex strategies of options are being traded in many exchanges which are called teji-

mandi, jota-phatak, bhav-bhav at different places in India (Vohra and Bagari,1998)

In that sense, the derivatives are not new to India and are also currently prevalent in

various markets including equities markets.

2.2.5 Is the existing capital market more safer than Derivatives?


World over, the spot markets in equities are operated on a principle of rolling settlement.

In this kind of trading, if you trade on a particular day (T), you have to settle these trades

on the third working day from the date of trading (T+3).

Futures market allow you to trade for a period of say 1 month or 3 months and allow you

to net the transaction taken place during the period for the settlement at the end of the

period. In India, most of the stock exchanges allow the participants to trade during one-

week period for settlement in the following week. The trades are netted for the settlement

for the entire one-week period. In that sense, the Indian markets are already operating the

futures style settlement rather than cash markets prevalent internationally.

In this system, additionally, many exchanges also allow the forward trading called badla

in Gujarati and Contango in English, which was prevalent in UK. This system is

prevalent currently in France in their monthly settlement markets. It allowed one to even

further increase the time to settle for almost 3 months under the earlier regulations. This

way, a curious mix of futures style settlement with facility to carry the settlement

obligations forward creates discrepancies.


The more efficient way from the regulatory perspective will be to separate out the

derivatives from the cash market i.e. introduce rolling settlement in all exchanges and at

the same time allow futures and options to trade. This way, the regulators will also be

able to regulate both the markets easily and it will provide more flexibility to the market

participants.

In addition, the existing system although futures style, does not ask for any margins from

the clients. Given the volatility of the equities market in India, this system has become

quite prone to systemic collapse. This was evident in the MS Shoes scandal. At the time

of default taking place on the BSE, the defaulting member of the BSE Mr.Zaveri had a

position close to Rs.18 crores. However, due to the default, BSE had to stop trading for a

period of three days. At the same time, the Barings Bank failed on Singapore Monetary

Exchange (SIMEX) for the exposure of more than US $ 20 billion (more than Rs.84,000

crore) with a loss of approximately US $ 900 million ( around Rs.3,800 crore). Although,

the exposure was so high and even the loss was also very big compared to the total

exposure on MS Shoes for BSE of Rs.18 crores, the SIMEX had taken so much margins

that they did not stop trading for a single minute.

2.3 Comparision of New System with Existing System5

Many people and brokers in India think that the new system of Futures & Options and

banning of Badla is disadvantageous and introduced early, but I feel that this new system

is very useful especially to retail investors. It increases the no of options investors for

investment. In fact it should have been introduced much before and NSE had approved it

but was not active because of politicization in SEBI.

The figure 2.1 –2.4 6shows how advantages of new system (implemented from June

20001) v/s the old system i.e.before June 2001

5 Source: Mr. Rajesh Gajra Senior writer- Intelligent Investor ([email protected])6 Source: Invest Monitor (Magazine) July 2001


New System Vs Existing System for Market Players

Figure 2.1

Speculators

Existing SYSTEM New

Approach Peril &Prize Approach Peril &Prize 1) Deliver based 1) Both profit & 1)Buy &Sell stocks 1)MaximumTrading, margin loss to extent of on delivery basis loss possibletrading& carry price change. 2) Buy Call &Put to premiumforward transactions. by paying paid2) Buy Index Futures premium hold till expiry.

Advantages Greater Leverage as to pay only the premium.

Greater variety of strike price options at a given time.

Figure 2.2

Arbitrageurs

Existing SYSTEM New

Approach Peril &Prize Approach Peril &Prize 1) Buying Stocks in 1) Make money 1) B Group more 1) Risk freeone and selling in whichever way the promising as still game. another exchange. Market moves. in weekly settlement forward transactions. 2) Cash &Carry


2) If Future Contract arbitrage continuesmore or less than Fair price

Fair Price = Cash Price + Cost of Carry.

Figure 2.3

Hedgers

Existing SYSTEM New

Approach Peril &Prize Approach Peril &Prize 1) Difficult to 1) No Leverage 1)Fix price today to buy 1) Additionaloffload holding available risk latter by paying premium. cost is onlyduring adverse reward dependant 2)For Long, buy ATM Put premium.market conditions on market prices Option. If market goes up,as circuit filters long position benefit elselimit to curtail losses. exercise the option. 3)Sell deep OTM call option with underlying shares, earn premium + profit with increase prcie

Advantages Availability of Leverage

Figure 2.4

Small Investors

Existing SYSTEM New

Approach Peril &Prize Approach Peril &Prize 1) If Bullish buy 1) Plain Buy/Sell 1) Buy Call/Put options 1) Downsidestocks else sell it. implies unlimited based on market outlook remains profit/loss. 2) Hedge position if protected & holding underlying upside stock unlimited.


Advantages Losses Protected.

3.0 SWAPSA contract between two parties, referred to as counter parties, to exchange two streams of

payments for agreed period of time. The payments, commonly called legs or sides, are

calculated based on the underlying notional using applicable rates. Swaps contracts also

include other provisional specified by the counter parties. Swaps are not debt instrument

to raise capital, but a tool used for financial management. Swaps are arranged in many

different currencies and different periods of time. US$ swaps are most common followed

by Japanese yen, sterling and Deutsche marks. The length of past swaps transacted has

ranged from 2 to 25 years.

3.1 Why did swaps emerge?

In the late 1970's, the first currency swap was engineered to circumvent the currency

control imposed in the UK. A tax was levied on overseas investments to discourage

capital outflows. Therefore, a British company could not transfer funds overseas in order

to expand its foreign operations without paying sizeable penalty. Moreover, this British

company had to take an additional currency risks arising from servicing a sterling debt

with foreign currency cash flows. To overcome such a predicament, back-to-back loans

were used to exchange debts in different currencies. For example, a British company

wanting to raise capital in the France would raise the capital in the UK and exchange its

obligations with a French company, which was in a reciprocal position. Though this type

of arrangement was providing relief from existing protections, one could imagine, the

task of locating companies with matching needs was quite difficult in as much as the cost

of such transactions was high. In addition, back-to-back loans required drafting multiple

loan agreements to state respective loan obligations with clarity. However this type of

arrangement lead to development of more sophisticated swap market of today.

Facilitators

The problem of locating potential counter parties was solved through dealers and brokers.

A swap dealer takes on one side of the transaction as counterparty. Dealers work for

investment, commercial or merchant banks. "By positioning the swap", dealers earn bid-


ask spread for the service. In other words, the swap dealer earns the difference between

the amount received from a party and the amount paid to the other party. In an ideal

situation, the dealer would offset his risks by matching one step with another to

streamline his payments. If the dealer is a counterparty paying fixed rate payments and

receiving floating rate payments, he would prefer to be a counterparty receiving fixed

payments and paying floating rate payments in another swap. A perfectly netted position

as just described is not necessary. Dealers have the flexibility to cover their exposure by

matching multiple parties and by using other tools such as futures to cover an exposed

position until the book is complete.

Swap brokers, unlike a dealer do not take on a swap position themselves but simply

locate counter parties with matching needs. Therefore, brokers are free of any risks

involved with the transactions. After the counter parties are located, the brokers negotiate

on behalf of the counter parties to keep the anonymity of the parties involved. By doing

so, if the swap transaction falls through, counter parties are free of any risks associated

with releasing their financial information. Brokers receive commissions for their services.

3.2 Swaps Pricing:

There are four major components of a swap price.

Benchmark price

Liquidity (availability of counter parties to offset the swap).

Transaction cost

Credit risk 7

Swap rates are based on a series of benchmark instruments. They may be quoted as a

spread over the yield on these benchmark instruments or on an absolute interest rate

basis. In the Indian markets the common benchmarks are MIBOR, 14, 91, 182 & 364 day

T-bills, CP rates and PLR rates.

7 Source: www.appliederivatives.com


Liquidity, which is function of supply and demand, plays an important role in swaps

pricing. This is also affected by the swap duration. It may be difficult to have counter

parties for long duration swaps, specially so in India Transaction costs include the cost of

hedging a swap. Say in case of a bank, which has a floating obligation of 91 day T. Bill.

Now in order to hedge the bank would go long on a 91 day T. Bill. For doing so the bank

must obtain funds. The transaction cost would thus involve such a difference.

Yield on 91 day T. Bill - 9.5%

Cost of fund (e.g.- Repo rate) – 10%

The transaction cost in this case would involve 0.5%

Credit risk must also be built into the swap pricing. Based upon the credit rating of the

counterparty a spread would have to be incorporated. Say for e.g. it would be 0.5% for an

AAA rating.

Swap Market Participation’s

Since swaps are privately negotiated products, there is no restriction on who can use the

market. However, parties with low credit quality have difficulty entering the market. This

is due to fact that they cannot be matched with counter parties who are willing to take on

their risks. In the U.S. many parties require their counter parties to have minimum assets

of $10 million. This requirement has become a standardized representation of "eligible

swap participants".

3.3 Introduction of Forward Rate Agreements and Interest

Rate Swaps

The Indian scene 8

Objective

To further deepen the money markets

To enable banks, primary dealers and all India financial institutions to hedge interest

rate risks.

These guidelines are intended to form the basis for development of Rupee derivative

products such as FRAs/IRS in the country. They have been formulated in consultation

8 Source: RBI Guidelines


with market participants. The guidelines are subject to review, on the basis of

development of FRAs/IRS market.

Accordingly, it has been decided to allow scheduled commercial banks (excluding

Regional Rural Banks), primary dealers and all -India financial institutions to undertake

FRAs/IRS as a product for their own balance sheet management and for market making

purposes.

Prerequisites

Participants are to ensure that appropriate infrastructure and risk management systems are

put in place. Further, participants should also set up sound internal control system

whereby a clear functional separation of trading, settlement, monitoring and control and

accounting activities is provided.

3.4 Description of the product

A Forward Rate Agreement (FRA) is a financial contract between two parties

exchanging or swapping a stream of interest payments for a notional principal amount on

settlement date, for a specified period from start date to maturity date. Accordingly, on

the settlement date, cash payments based on contract (fixed) and the settlement rate, are

made by the parties to one another. The settlement rate is the agreed benchmark/reference

rate prevailing on the settlement date.

An Interest Rate Swap (IRS) is a financial contract between two parties exchanging or

swapping a stream of interest payments for a notional principal amount of multiple

occasions on specified periods. Accordingly, on each payment date that occurs during the

swap period-Cash payments based on fixed/floating and floating rates are made by the

parties to one another.

Currency swaps can be defined as a legal agreement between two or more parties to

exchange interest obligation or interest receipts between two different currencies. It

involves three steps:

Initial exchange of principal between the counter parties at an agreed upon rate of

exchange which is usually based on spot exchange rate. This exchange is optional and

its sole objective is to establish the quantum of the respective principal amounts for


the purpose for calculating the ongoing payments of interest and to establish the

principal amount to be re-exchanged at the maturity of the swap.

Ongoing exchange of interest at the rates agreed upon at the outset of the transaction.

Re-exchange of principal amount on maturity at the initial rate of exchange.

This straight forward, three step process results in the effective transformation of the debt

raised in one currency into a fully hedged liability in other currency.

Participants

Schedule commercial banks.

Primary dealers

All India financial institutions

3.5 Currency Swaps in India

RBI in its slack season credit policy '97 allowed the authorized dealers to arrange

currency swap without its prior approval. This was to enable those requiring long-term

forward cover to hedge themselves without altering the external liability of the country.

Prior to this policy RBI had been approving rupee foreign currency swaps between

corporates on a case basis, but no such swaps were taking place.

RBI in its process of making the Indian corporates globally competitive has simplified

their access to this instrument by making changes in its credit policy. But despite an

easing regulation, swaps have not hit the market in a big way.

India has a strong dollar-rupee forward market with contracts being traded for one, two,

six-month expiration. Daily trading volume on this forward market is around $500

million a day. Indian users of hedging services are also allowed to buy derivatives

involving other currencies on foreign markets. Outside India, there is a small market for

cash –settled forward contracts on the dollar –rupee exchange rate.

While studying swaps in the Indian context, the counter parties involved are Indian

corporates and the swap dealers are the Authorized dealers of foreign exchange, i.e., the

banks allowed by RBI to carry out the swaps. These banks form the counterparty to the


corporates on both sides of the swap and keep a spread between the interest rates to be

received and offered. One of the currencies involved is the Indian rupee and the other

could be any foreign currency. The interest rate on the rupee is most likely to be fixed,

and on foreign currency it could be either fixed or floating.

3.5.1 The Players

Swaps are instruments, which allow the user to hedge - that are to offset risk or to take

risk deliberately in the expectation of making profit. The user in this case would be any

corporate having a foreign exchange exposure/ a risk. A foreign exchange exposure will

arise out of the mismatch between the currency of inflow and outflow. The outflow being

considered here is the interest and the principal payment on the borrowings of the

corporates. Corporates having such currency mismatches would be of the following types

3.5.2Corporates with rupee loan and forex revenue

Mainly the exporters would fall in this category. Corporates with foreign subsidiaries

would also be having forex revenues but due to cheaper availability of funds abroad, it is

unlikely that these subsidiaries would be funded by a rupee loan. Thus the main players

meeting this criterion would be the exporters. The main players in the Indian market are

Tata Exports, Hindustan Levers Ltd., ITC Ltd., and Nestle Indian Ltd. among the others.

3.5.3 Corporates with forex loan and rupee revenue

The corporates having foreign currency loan could further be classified into two groups.

One which have net imports and thus may have raised loans to meet their import

requirements, for example Bharat Heavy Electricals Ltd., Apollo Tyres Ltd., Tata Power

Co. Ltd.

Two, which do not have net imports but have raised foreign currency loan for funding

requirements, for example Arvind Mills Ltd., Ballarpur Industries etc.

3.5.4 Corporates with no foreign exposure

There may be corporates with no existing exposure but willing to take up an exposure in

an expectation of making profit out of this transaction. Thus they would be willing to

swap their rupee loan with forex loan and book in forward cover or make the payments


on spot basis on the day of disbursements. These corporates may also consider the option

of raising new loans in foreign currency and swap a rupee loan if it turns out to be

cheaper option. Thus many corporates would fall under this category.

3.5.5 Banks

Banks act as the authorized dealers and are instrumental in arranging swaps. They have to

take the swaps on their books. A bank would enter into swap with a party and then try to

find another with opposite requirement to hedge itself against any fluctuation in exchange

rates. They would normally keep a spread between the offer and bid rate thus make profit

from transaction. They also take up the credit risk of counterparties.

3.6 The needs of the players and how currency swaps help meet

these needs

3.6.1 To manage the exchange rate risk

Since the international trade implies returns and payments in a variety of currencies

whose relative values may fluctuate it involves taking foreign exchange risk. The players

mentioned above are facing this risk. A key question facing the players then is whether

these exchange risks are so large as to affect their business. A related question is what, if

any, special strategies should be followed to reduce the impact of foreign exchange risk.

One-way to minimize the long-term risk of one currency being worth more or less in the

future is to offset the particular cash flow stream with an opposite flow in the same

currency. The currency swap helps to achieve this without raising new funds; instead it

changes existing cash flows.

3.6.2 To lower financing cost

Currency swaps can be used to reduce the cost of loan. The following example deals with

such a case.

Consider two Indian corporates A & B. Corporate A is an exporter with a rupee loan at

14% fixed rate. B has a dollar loan at LIBOR + 0.25% floating rate. Due to difference in

the credit rating of the two companies, the rates at which the loans are available to them

are different. A has access to 14% rupee loan and dollar loan at LIBOR + 0.25%.

A would like to convert its rupee loan into a dollar loan, to reverse its revenue in dollars

and B would like to convert the dollar loan into a fixed rupee loan thus crystallizing its


cost of borrowing. They can enter into a swap and reduce the cost compared to what it

would have been if they had taken a direct loan in the desired currencies.

- Comparative advantage

Company A Exporter Company B

Options: Options:

Borrow ruppe at 13% Borrow ruppe at 14.5%

Borrow dollars at LIBOR +100 bps Borrow dollars at LIBOR +200 bps

Company A has an absolute advantage over B in both the markets/ rates. The advantage

in terms of rupee funds is 150 bps while it is 100 bps in case of dollar rates. Thus B has a

comparative advantage in terms of dollar rates.

Now as A is an exporter he would be more interested in a dollar denominated loan to

offset his future receivables.

Therefore it would be advantageous if A would borrow at rupee rates and B borrows at

LIBOR rates. Then they may go in for a currency swap. The net gain arising out of such a

swap will be 50 bps, which may be shared between the parties.

The swap will thus result in A paying B a floating rate of LIBOR + 75 bps in return for a

13% fixed rupee rate. The swap will take place on a notional principal basis.

The effective cost for A is LIBOR + 75 bps and for B it is 14.25%. The effective cost for

A is 12.75%. This results into a net saving of 25 bps for both the parties.

Figure 3.1

LIBOR +75 bps

Company A Company B12.75% in INR

13% in INR Libor +200 bps

- To access restricted markets

Many countries have restrictions on the type of borrowers that can raise funds in their

bond markets. Foe example an Indian firm exporting goods to Japan may wish to issue

bonds in yen to form a natural hedge by reversing their cash flows. To issue a yen bond,


the borrower must qualify for a single A credit rating. If the company does not qualify in

this regard it would fail to issue yen denominated bond.

By issuing bonds in the rupee market and then entering into a currency swap, the firm can

meet its expectation of raising a yen denominated loan.

3.6.3 Swaps for reducing the cost of borrowing

With the introduction of rupee derivatives the Indian corporates can attempt to reduce

their cost of borrowing and thereby add value. A typical Indian case would be a corporate

with a high fixed rate obligation.

Eg.

Mehta Ltd. an AAA rated corporate, 3 years back had raised 4-year funds at a fixed rate

of 18.5%. Today a 364-day T. bill is yielding 10.25%, as the interest rates have come

down. The 3-month MIBOR is quoting at 10%.

Fixed to floating 1 year swaps are trading at 50 bps over the 364-day T. bill vs 6-month

MIBOR.

The treasurer is of the view that the average MIBOR shall remain below 18.5% for the

next one year.

The firm can thus benefit by entering into an interest rate fixed for floating swap,

whereby it makes floating payments at MIBOR and receives fixed payments at 50 bps

over a 364 day treasury yield i.e. 10.25 + 0.50 = 10.75 %.

Figure 3.2

Fixed 10.75 Mehta Ltd Counter Party

3 Months MIBOR

18.75%s MIBOR


The effective cost for Mehta Ltd. = 18.5 + MIBOR - 10.75

= 7.75 + MIBOR

At the present 3m MIBOR at 10%, the effective cost is = 10 + 7.75 = 17.75%

The gain for the firm is (18.5 - 17.75) = 0.75 %

The risks involved for the firm are

- Default/ credit risk of counterparty. This may be ignored, as the counterparty is a bank.

This risk involves losses to the extent of the interest rate differential between fixed and

floating rate payments.

- The firm is faced with the risk that the MIBOR goes beyond 10.75%. Any rise beyond

10.75% will raise the cost of funds for the firm. Therefore it is very essential that the firm

hold a strong view that MIBOR shall remain below 10.75%. This will require continuous

monitoring on the path of the firm.

How does the bank benefit out of this transaction?

The bank either goes for another swap to offset this obligation and in the process earn a

spread. The bank may also use this swap as an opportunity to hedge its own floating

liability. The bank may also leave this position uncovered if it is of the view that MIBOR

shall rise beyond 10.75%.

Taking advantage of future views/ speculation

If a bank holds a view that interest rate is likely to increase and in such a case the return

on fixed rate assets will not increase, it will prefer to swap it with a floating rate interest.

It may also swap floating rate liabilities with a fixed rate.

3.7 Factors to be looked at while doing a swap

Though swaps can be used in the above conditions effectively, corporates need to look at

a few factors before deciding to swap.

The estimated net exposure


They need to estimate the net exposure that they are likely to have in the future.

Projecting the growth in exports/ imports, taking into account the changes in management

and government policies can do this.

Expected range of exchange rates

This can be determined by a fundamental and technical analysis. For fundamental

analysis one needs to keep track of the balance of payment condition, GDP growth rate,

etc. of the country. The technical factors look at past trends and expected demand-supply

position. Other factors like political stability also needs to be considered.

Expected interest rates

Since currency swaps include exchange of interest payments, the interest rates also need

to be traced. By keeping an eye on the yield curve of long term bonds and the macro

economic variables of different countries, the interest rates can be estimated.

Amount of cover to be taken

Having estimated the amount of exposure, the expected exchange rates and the interest

rates, the parties can determine the risks involved and can decide upon the amount of

cover to be taken. This shall depend on the management policy whether they believe in

minimizing the risk for a given level of return or maximizing the gain for a given level of

risk. The risk taking capability of a corporate will depend upon the financial backup to

absorb the losses, if any, the availability of time and resources to monitor the forex

market.

3.8 Market Report- Issues of Concern

Unfortunately, money markets as a whole are not developed. The biggest problem

continues to be the structure of the money market. Two-way quotes are a fundamental

necessity for a proper yield curve to develop and a reference rate to be established. The

RBI does not encourage lend/borrow transaction on the same day. While foreign banks

and some of the new banks are perennial borrowers in the inter-bank market, several

nationalised banks and institutions are perennial lenders. This leaves the primary dealers

to do the trading. But their limited funds do not enable them to become large players.

This gives rise to uni-directional players who are averse to two-way quotes. This deters

the development of a benchmark around which a term market can evolve.


Right now, whatever trading is done is through the fixed rate. For IRS to happen there

should be swaps in maturities. A benchmarking has to be done and for that we need a

correct reference rate, which will have to evolve beyond the overnight rate (MIBOR).

That can happen only if a term money market is in place.

In India fixed rates are aplenty with banks and institutions borrowing and lending at fixed

rates. They also adopt floating rates (Prime Lending Rate or PLR) while lending. But the

PLR has two crucial deficiencies compared to rates like LIBOR: PLR is not a market

related rate, but determined, somewhat arbitrarily, on the basis of the bank rate. Besides

there are no two-way quotes in PLR, in the absence of which swap deals virtually become

infructuous. Rates like LIBOR, Fed Funds Rate/ T.Bill Rate are those at which banks are

prepared to lend and borrow in any currency.

In India too, such a market does exist for the rupee- the call money market. Banks

borrow/lend at market determined rates. But where the Indian money market differs from

other major financial centers is that, in the latter money is available for periods ranging

from 1 or 7 days to 3, 6 and 12 months, whereas in India, rupee is available for a day or

two, up to a maximum period of 13 days, as a general rule. The reason being the

fortnightly reserve requirements.

Another deficiency is the lack of integration with the foreign exchange (FX) markets. In

order to protect and control the exchange rate of the rupee, strong silos have been created.

Forward premium between the rupee and another foreign currency does not reflect the

interest rate differential. If anything, it reflects the estimated risk of depreciation of the

local unit against the dollar. This gives rise to significant arbitrage opportunities between

the two markets, which are protected through the RBI diktat. At present, the tenors

available in the IRS market are short and the benchmark limited to only one, the Mumbai

Inter-bank Offer Rate (MIBOR).

3.9 Some swaps in near future9

March 10 2001

9 Source: www.economictimes.com


ICICI inks 5-year rupee IRS with Citibank

ICICI has entered into a five-year rupee interest rate swap with Citibank. This is the

fourth long-term swap deal in the IRS market during the fortnight.

The ICICI-Citibank swap deal has a notional amount of Rs 50 crore. The fixed portion of

the swap is based on the yield on the four-year government security, while the floating

rate is based on the one-year G-sec yield. “The floating rate will be reset on an annual

basis, for which five securities have been identified to provide a perfect residual

maturity,” said an ICICI official.

11 MAY 2001

Vysya Bank, L&T in Rs 10-cr overnight index swap deal

VYSYA Bank and Larsen & Toubro have entered into an overnight index swap (OIS)

transaction for Rs 10 crore. The one-year swap has Vysya Bank paying 8.75 per cent

against the compounded NSE Mibor to L&T. The deal, brokered by eMecklai, was done

over the internet. The verification of the swap differences will be carried out quarterly

with settlement at maturity.

17 FEBRUARY Jet swaps $340-m floating loan with Credit LyonnaisGeorge Cherian

CREDIT Lyonnais and Jet Airways have concluded the largest interest rate swap in the

country. A total of $340m of the air tax operator’s outstanding foreign currency floating

rate loans has been swapped to fixed/ floating via a structured interest rate swap spread

over four years.

It will insulate Jet Airways against rising interest rates. It will also give Jet Airways the

opportunity to take advantage of falling interest rates in later years. The swap, which has

been executed in two tranches of $200m and $140m, is the largest ever derivatives

transaction in the domestic market

4.0 Forward contracts & Futures & OptionsA forward contract is an agreement to buy or sell an asset on a specified date for a

specified price. One of the parties to the contract assumes a long position and agrees to

buy the underlying asset on a certain specified future date for a certain specified price.

The other party assumes a short position and agrees to sell the asset on the same date for


the same price. Other contract details like delivery date, price and quantity are negotiated

bilaterally by the parties to the contract. The forward contracts are normally traded

outside the exchanges.

The salient features of forward contracts are:

They are bilateral contracts and hence exposed to counter–party risk.

Each contract is custom designed, and hence is unique in terms of contract size,

expiration date and the asset type and quality.

The contract price is generally not available in public domain.

On the expiration date, the contract has to be settled by delivery of the asset.

If the party wishes to reverse the contract, it has to compulsorily go to the same

counter-party, which often results in high prices being charged.

However forward contracts in certain markets have become very standardized, as in the

case of foreign exchange, thereby reducing transaction costs and increasing transactions

volume. This process of standardization reaches its limit in the organized futures market.

Forward contracts are very useful in hedging and speculation. The classic hedging

application would be that of an exporter who expects to receive payment in dollars three

months later. He is exposed to the risk of exchange rate fluctuations. By using the

currency forward market to sell dollars forward, he can lock on to a rate today and reduce

his uncertainty. Similarly an importer who is required to make a payment in dollars two

months hence can reduce his exposure to exchange rate fluctuations by buying dollars

forward.

If a speculator has information or analysis, which forecasts an upturn in a price, then he

can go long on the forward market instead of the cash market. The speculator would go

long on the forward, wait for the price to rise, and then take a reversing transaction to

book profits. Speculators may well be required to deposit a margin upfront. However, this

is generally a relatively small proportion of the value of the assets underlying the forward

contract. The use of forward markets here supplies leverage to the speculator.

4.1 Limitations of forward markets


Forward markets world-wide are afflicted by several problems:

Lack of centralization of trading

Illiquidity, and Counter party risk

In the first two of these, the basic problem is that of too much flexibility and generality.

The forward market is like a real estate market in that any two consenting adults can form

contracts against each other. This often makes them design terms of the deal, which are

very convenient in that specific situation, but makes the contracts non-tradable.

Counterparty risk arises from the possibility of default by any one party to the

transaction. When one of the two sides to the transaction declares bankruptcy, the other

suffers. Even when for-ward markets trade standardized contracts, and hence avoid the

problem of illiquidity, still the counterparty risk remains a very serious issue.

4.2 Introduction to futures

Futures markets were designed to solve the problems that exist in forward markets. A

futures contract is an agreement between two parties to buy or sell an asset at a certain

time in the future at a certain price. But unlike forward contracts, the futures contracts are

standardized and exchange traded. To facilitate liquidity in the futures contracts, the

exchange specifies certain standard features of the contract. It is a standardized contract

with standard underlying instrument, a standard quantity and quality of the underlying

instrument that can be delivered, (or which can be used for reference purposes in

settlement) and a standard timing of such settlement. A futures contract may be offset

prior to maturity by entering into an equal and opposite transaction. More than 99% of

futures transactions are offset this way.

The standardized items in a futures contract are: -

Quantity of the underlying

Quality of the underlying

The date and the month of delivery

The units of price quotation and minimum price change

Location of settlement


4.3 Distinction between futures and forwards contracts

Forward contracts are often confused with futures contracts. The confusion is primarily

because both serve essentially the same economic functions of allocating risk in the

presence of future price uncertainty. However futures are a significant improvement over

the forward contracts as they eliminate counter party risk and offer more liquidity. Table

3.1 lists the distinction between the two.

Table 4.1 Distinction between futures and forwards 10

4.4 Futures Terminology

Spot price: The price at which an asset trades in the spot market.

Futures price: The price at which the futures contract trades in the futures market.

Contract cycle: The period over which a contract trades. The index futures contracts

on the NSE have one-month, two-months and three-months expiry cycles, which

expire on the last Thursday of the month. Thus a January expiration contract expires

on the last Thursday of January and a February expiration contract ceases trading on

the last Thursday of February. On the Friday following the last Thursday, a new

contract having a three-month expiry is introduced for trading.

Expiry date: It is the date specified in the futures contract. This is the last day on

which the contract will be traded, at the end of which it will cease to exist.

Contract size: The amount of asset that has to be delivered under one contract. For

in-stance, the contract size on NSE’s futures market is 200 Nifties.

Basis: In the context of financial futures, basis can be defined as the futures price

minus the spot price. There will be a different basis for each delivery month for each

10 Source: Derivatives in India FAQ’s by Ajay Shah & Susan Thomas

Futures Forwards

Trade on an organized exchange OTC in nature

Standardized contract terms Customised contract terms

Hence more liquid Hence less liquid

Requires margin payments No margin payment


contract. In a normal market, basis will be positive. This reflects that futures prices

normally exceed spot prices.

Cost of carry: The relationship between futures prices and spot prices can be

summarized in terms of what is known as the cost of carry. This measures the storage

cost plus the interest that is paid to finance the asset less the income earned on the

asset.

Initial margin: The amount that must be deposited in the margin account at the time

a futures contract is first entered into is known as initial margin.

Marking-to-market: In the futures market, at the end of each trading day, the margin

ac-count is adjusted to reflect the investor’s gain or loss depending upon the futures

closing price. This is called marking–to–market.

Maintenance margin: This is somewhat lower than the initial margin. This is set to

ensure that the balance in the margin account never becomes negative. If the balance

in the margin account falls below the maintenance margin, the investor receives a

margin call and is expected to top up the margin account to the initial margin level

before trading commences on the next day.

4.5 Introduction to options

In this section, we look at the next derivative product to be traded on the NSE, namely

options. Options are fundamentally different from forward and futures contracts. An

option gives the holder of the option the right to do something. The holder does not have

to exercise this right. In contrast, in a forward or futures contract, the two parties have

committed themselves to doing something. Whereas it costs nothing (except margin

requirements) to enter into a futures contract, the purchase of an option requires an up–

front payment.

4.5.1 History of options

Although options have existed for a long time, they were traded OTC, without much

knowledge of valuation. Today exchange-traded options are actively traded on stocks,

stock indexes, foreign currencies and futures contracts. The first trading in options began


in Europe and the US as early as the eighteenth century. It was only in the early 1900s

that a group of firms set up what was known as the put and call Brokers and Dealers

Association with the aim of providing a mechanism for bringing buyers and sellers

together. If someone wanted to buy an option, he or she would contact one of the member

firms.

The firm would then attempt to find a seller or writer of the option either from its own

clients or those of other member firms. If no seller could be found, the firm would

undertake to write the option itself in return for a price. This market however suffered

from two deficiencies. First, there was no secondary market and second, there was no

mechanism to guarantee that the writer of the option would honor the contract. It was in

1973, that Black, Merton and Scholes invented the famed Black Scholes formula. In

April 1973, CBOE was set up specifically for the purpose of trading options. The market

for options developed so rapidly that by early ’80s, the number of shares underlying the

option contract sold each day exceeded the daily volume of shares traded on the NYSE.

Since then, there has been no looking back.

4.6 Option Terminology

Index options: These options have the index as the underlying. Some options are

European while others are American. Like index futures contracts, index options

contracts are also cash settled.

Stock options: Stock options are options on individual stocks. Options currently

trade on over 500 stocks in the United States. A contract gives the holder the right to

buy or sell shares at the specified price.

Buyer of an option: The buyer of an option is the one who by paying the option

premium buys the right but not the obligation to exercise his option on the

seller/writer.

Writer of an option: The writer of a call/put option is the one who receives the

option premium and is thereby obliged to sell/buy the asset if the buyer exercises on

him. There are two basic types of options, call options and put options. Call option: A

call option gives the holder the right but not the obligation to buy an asset by a certain


date for a certain price. Put option: A put option gives the holder the right but not the

obligation to sell an asset by a certain date for a certain price.

Option price: Option price is the price which the option buyer pays to the option

seller.

Expiration date: The date specified in the options contract is known as the

expiration date, the exercise date, the strike date or the maturity.

Strike price: The price specified in the options contract is known as the strike price

or the exercise price.

American options: American options are options that can be exercised at any time

upto the expiration date. Most exchange-traded options are American.

European options: European options are options that can be exercised only on the

expiration date itself. European options are easier to analyze than American options,

and properties of an American option are frequently deduced from those of its

European counterpart.

In-the-money option: An in-the-money (ITM) option is an option that would lead to

a positive cashflow to the holder if it were exercised immediately. A call option on

the index is said to be in-the-money when the current index stands at a level higher

than the strike price (i.e. spot price > strike price). If the index is much higher than the

strike price, the call is said to be deep ITM. In the case of a put, the put is ITM if the

index is below the strike price.

At-the-money option: An at-the-money (ATM) option is an option that would lead

to zero cashflow if it were exercised immediately. An option on the index is at-the-

money when the current index equals the strike price (i.e. spot price = strike price)._

Out-of-the-money option: An out-of-the-money (OTM) option is an option that

would lead to a negative cashflow it it were exercised immediately. A call option on

the index is out-of- the-money when the current index stands at a level which is less

than the strike price (i.e. spot price < strike price). If the index is much lower than the

strike price, the call is said to be deep OTM. In the case of a put, the put is OTM if

the index is above the strike price.

Intrinsic value of an option: The option premium can be broken down into two

components - intrinsic value and time value. The intrinsic value of a call is the

amount the option is ITM, if it is ITM. If the call is OTM, its intrinsic value is zero.


Putting it another way, the intrinsic value of a call isN½P which means the intrinsic

value of a call is Max [0, (St – K)] which means the intrinsic value of a call is the (St –

K). Similarly, the intrinsic value of a put is Max [0, (K -St )] ,i.e. the greater of 0 or

(K - St ). K is the strike price and St is the spot price.

Time value of an option: The time value of an option is the difference between its

premium and its intrinsic value. A call that is OTM or ATM has only time value.

Usually, the maximum time value exists when the option is ATM. The longer the

time to expiration, the greater is a call’s time value, all else equal. At expiration, a call

should have no time value. 11

Table 4.2 Distinction between futures and options

Futures Options

Exchange traded, with novation Same as futures.

Exchange defines the product Same as futures.

Price is zero, strike price moves Strike price is fixed, price moves.

Price is zero Price is always positive.

Linear payoff Nonlinear payoff.

Both long and short at risk Only short at risk.

4.7 Futures and options

An interesting question to ask at this stage is - when would one use options instead of

futures? Options are different from futures in several interesting senses.

At a practical level, the option buyer faces an interesting situation. He pays for the option

in full at the time it is purchased. After this, he only has an upside. There is no possibility

of the options position generating any further losses to him (other than the funds already

paid for the option). This is different from futures, which is free to enter into, but can

11 Source: www.derivativesindia.com


generate very large losses. This characteristic makes options attractive to many

occasional market participants, who cannot put in the time to closely monitor their futures

positions.

Buying put options is buying insurance. To buy a put option on Nifty is to buy insurance,

which reimburses the full extent to which Nifty drops below the strike price of the put

option. This is attractive to many people, and to mutual funds creating “guaranteed return

products”. The Nifty index fund industry will find it very useful to make a bundle of a

Nifty index fund and a Nifty put option to create a new kind of a Nifty index fund, which

gives the investor protection against extreme drops in Nifty.

4.8 Index derivatives

Index derivatives are derivative contracts, which derive their value from an underlying

index. The two most popular index derivatives are index futures and index options. Index

derivatives have become very popular worldwide. In his report, Dr.L.C.Gupta attributes

the popularity of index derivatives to the advantages they offer.

Institutional and large equity-holders need portfolio-hedging facility. Index–

derivatives are more suited to them and more cost–effective than derivatives based on

individual stocks. Pension funds in the US are known to use stock index futures for

risk hedging purposes.

Index derivatives offer ease of use for hedging any portfolio irrespective of its

composition.

Stock index is difficult to manipulate as compared to individual stock prices, more so

in India, and the possibility of cornering is reduced. This is partly because an

individual stock has a limited supply, which can be cornered.

Stock index, being an average, is much less volatile than individual stock prices. This

implies much lower capital adequacy and margin requirements.

Index derivatives are cash settled, and hence do not suffer from settlement delays and

problems related to bad delivery, forged/fake certificates.


The L.C.Gupta committee which was setup for developing a regulatory framework for

derivatives trading in India had suggested a phased introduction of derivative products in

the following order:

1. Index futures

2. Index options

3. Options on individual stocks

With all the above infrastructure in place, trading of index futures and index options

commenced at NSE in June 2000 and June 2001 respectively.

5.0 Payoff & Pricing of Futures and

OptionsA payoff is the likely profit/loss that would accrue to a market participant with change in

the price of the underlying asset. This is generally depicted in the form of payoff

diagrams which show the price of the underlying asset on the X–axis and the

profits/losses on the Y–axis. In this section we shall take a look at the payoffs for buyers

and sellers of futures and options.

5.1 Payoff for futures

Futures contracts have linear payoffs. In simple words, it means that the losses as well as

profits for the buyer and the seller of a futures contract are unlimited.

These linear payoffs are fascinating as they can be combined with options and the

underlying to generate various complex payoffs.

5.1.1 Payoff for buyer of futures: Long futures

The payoff for a person who buys a futures contract is similar to the payoff for a person

who holds an asset. He has a potentially unlimited upside as well as a potentially

unlimited downside.

Take the case of a speculator who buys a two-month Nifty index futures contract when

the Nifty stands at 1220. The underlying asset in this case is the Nifty portfolio. When the


index moves up, the long futures position starts making profits, and when the index

moves down it starts making losses. Figure 5.1 shows the payoff diagram for the buyer of

a futures contract.

5.1.2 Payoff for seller of futures: Short futures

The payoff for a person who sells a futures contract is similar to the payoff for a person

who shorts an asset. He has a potentially unlimited upside as well as a potentially

unlimited downside. Take the case of a speculator who sells a two-month Nifty index

futures contract when the Nifty stands at 1220. The underlying asset in this case is the

Nifty portfolio. When the index moves down, the short futures position starts making

profits, and when the index moves up, it starts making losses. Figure 5.2 shows the

payoff diagram for the seller of a futures contract.

Figure 5.1 Payoff for a buyer of Nifty futures

The figure shows the profits/losses for a long futures position. The investor bought futures when the index was at 1220. If the index goes up, his futures position starts making profit. If the index falls, his futures position starts showing losses.

Profit

1220 0 Nifty

Loss

Figure 5.2 Payoff for a seller of Nifty futures

The figure shows the profits/losses for a short futures position. The investor sold futures when the index was at 1220. If the index goes down, his futures position starts making profit. If the index rises, his futures position starts showing losses.

Profit

1220 0 Nifty


Loss

5.2 Options payoffs

The optionality characteristic of options results in a non-linear payoff for options. In

simple words, it means that the losses for the buyer of an option are limited, however the

profits are potentially unlimited. For a writer, the payoff is exactly the opposite. His

profits are limited to the option premium, however his losses are potentially unlimited.

These non-linear payoffs are fascinating as they lend themselves to be used to generate

various payoffs by using combinations of options and the underlying. We look here at the

six basic payoffs.

5.2.1 Payoff profile of buyer of asset: Long asset

In this basic position, an investor buys the underlying asset, Nifty for instance, for 1220,

and sells it at a future date at an unknown price,S4 it is purchased, the investor is said to

be “long” the asset. Figure 5.3 shows the payoff for a long position on the Nifty.12

Figure 5.3 Payoff for investor who went Long Nifty at 1220

The figure shows the profits/losses from a long position on the index. The investor bought the index at 1220. If the index goes up, he profits. If the index falls he looses.

Profit +60

0 1160 1220 1280 Nifty

-60

Loss

5.2.2 Payoff profile for seller of asset: Short asset

12 Source: NSE Derivatives Core Module


In this basic position, an investor shorts the underlying asset, Nifty for instance, for 1220,

and buys it back at a future date at an unknown price S4 Once it is sold, the investor is

said to be “short” the asset. Figure 5.4 shows the payoff for a short position on the Nifty.

Figure 5.4 Payoff for investor who went Short Nifty at 1220

The figure shows the profits/losses from a short position on the index. The investor sold the index at 1220. If the index falls, he profits. If the index rises, he looses.

Profit

+60

0 1160 1220 1280 Nifty

-60

Loss

5.2.3 Payoff profile for buyer of call options: Long call

A call option gives the buyer the right to buy the underlying asset at the strike price

specified in the option. The profit/loss that the buyer makes on the option depends on the

spot price of the underlying. If upon expiration, the spot price exceeds the strike price, he

makes a profit. Higher the spot price, more is the profit he makes. If the spot price of the

underlying is less than the strike price, he lets his option expire un-exercised. His loss in

this case is the premium he paid for buying the option. Figure 5.5 gives the payoff for the

buyer of a three month call option (often referred to as long call) with a strike of 1250

bought at a premium of 86.60.

5.2.4 Payoff profile for writer of call options: Short call

A call option gives the buyer the right to buy the underlying asset at the strike price

specified in the option. For selling the option, the writer of the option charges a premium.

The profit/loss that the buyer makes on the option depends on the spot price of the

underlying. Whatever is the buyer’s profit is the seller’s loss. If upon expiration, the spot


price exceeds the strike price, the buyer will exercise the option on the writer. Hence as

the spot price increases the writer of the option starts making losses. Higher the spot

price, more is the loss he makes. If upon expiration the spot price of the underlying is less

than the strike price, the buyer lets his option expire un-exercised and the writer gets to

keep the premium. Figure 5.6 gives the payoff for the writer of a three month call option

(often referred to as short call) with a strike of 1250 sold at a premium of 86.60.

Figure 5.5 Payoff for buyer of call option

The figure shows the profits/losses for the buyer of a three-month Nifty 1250 call option. As can be seen, as the spot Nifty rises, the call option is in-the-money. If upon expiration, Nifty closes above the strike of 1250, the buyer would exercise his option and profit to the extent of the difference between the Nifty-close and the strike price. The profits possible on this option are potentially unlimited. However if Nifty falls below the strike of 1250, he lets the option expire. His losses are limited to the extent of the premium he paid for buying the option.

Profit

1250 0 Nifty

86.60

Loss

Figure 5.6 Payoff for writer of call option

The figure shows the profits/losses for the seller of a three-month Nifty 1250 call option. As the spot Nifty rises, the call option is in-the-money and the writer starts making losses. If upon expiration, Nifty closes above the strike of 1250, the buyer would exercise his option on the writer who would suffer a loss to the extent of the difference between the Nifty-close and the strike price. The loss that can be incurred by the writer of the option is potentially unlimited, whereas the maximum profit is limited to the extent of the up-front option premium of Rs.86.60 charged by him.

Profit

86.60 1250 0 Nifty


Loss

5.2.5 Payoff profile for buyer of put options: Long put

A put option gives the buyer the right to sell the underlying asset at the strike price

specified in the option. The profit/loss that the buyer makes on the option depends on the

spot price of the underlying. If upon expiration, the spot price is below the strike price, he

makes a profit. Lower the spot price, more is the profit he makes. If the spot price of the

underlying is higher than the strike price, he lets his option expire un-exercised. His loss

in this case is the premium he paid for buying the option. Figure 5.7 gives the payoff for

the buyer of a three month put option (often referred to as long put) with a strike of 1250

bought at a premium of 61.70.

Figure 5.7 Payoff for buyer of put option

The figure shows the profits/losses for the buyer of a three-month Nifty 1250 put option. As can be seen, as the spot Nifty falls, the put option is in-the-money. If upon expiration, Nifty closes below the strike of 1250, the buyer would exercise his option and profit to the extent of the difference between the strike price and Nifty-close. The profits possible on this option can be as high as the strike price. However if Nifty rises above the strike of 1250, he lets the option expire. His losses are limited to the extent of the premium he paid for buying the option.

Profit

1250 0 Nifty61.70

Loss

5.2.6 Payoff profile for writer of put options: Short put


A put option gives the buyer the right to sell the underlying asset at the strike price

specified in the option. For selling the option, the writer of the option charges a premium.

The profit/loss that the buyer makes on the option depends on the spot price of the

underlying. Whatever is the buyer’s profit is the seller’s loss. If upon expiration, the spot

price happens to be below the strike price, the buyer will exercise the option on the

writer. If upon expiration the spot price of the underlying is more than the strike price, the

buyer lets his option expire un-exercised and the writer gets to keep the premium. Figure

5.8 gives the payoff for the writer of a three-month put option (often referred to as short

put) with a strike of 1250 sold at a premium of 61.70.

Figure 5.8 Payoff for writer of put optionThe figure shows the profits/losses for the seller of a three-month Nifty 1250 put option. As the spot Nifty falls, the put option is in-the-money and the writer starts making losses . If upon expiration, Nifty closes below the strike of 1250, the buyer would exercise his option on the writer who would suffer a loss to the extent of the difference between the strike price and Nifty-close. The loss that can be incurred by the writer of the option is a maximum extent of the strike price(Since the worst that can happen is that the asset price can fall to zero) whereas the maximum profit is limited to the extent of the up-front option premium of Rs.61.70 charged by him.

Profit

61.70 1250 0 Nifty

Loss

5.3 Pricing Index FuturesStock index futures began trading on NSE on the 12th June 2000. Ever since, the

volumes and open interest has been steadily growing. Looking at the futures prices on

NSE’s market, have you ever felt the need to know whether the quoted prices are a true

reflection of the underlying index’s price? Have you wondered whether you could make

risk-less profits by arbitraging between the underlying and futures markets? If so, you


need to know the cost-of-carry to understand the dynamics of pricing that constitute the

estimation of fair value of futures.

5.3.1 The cost of carry model

We use fair value calculation of futures to decide the no-arbitrage limits on the price of a

futures contract. This is the basis for the cost-of-carry model where the price of the

contract is defined as:

F=S+C

Where:

F: Futures price

S: Spot price

C: Holding costs or carry costs

This can also be expressed as:

F=s (1+r) T

Where:

r: Cost of financing

T: Time till expiration

If F < s (1+r) T or F > s (1+r) T, arbitrage opportunities would exist i.e. whenever the

futures price moves away from the fair value, there would be chances for arbitrage. We

know what the spot and future prices are, but what are the components of holding cost?

The components of holding cost vary with contracts on different assets. At times the

holding cost may even be negative. In the case of commodity futures, the holding cost is

the cost of financing plus cost of storage and insurance purchased etc. In the case of

equity futures, the holding cost is the cost of financing minus the dividends returns.

Note: In the futures pricing examples worked out in this book, we are using the concept

of discrete compounding, where interest rates are compounded at discrete intervals, for

example, annually or semiannually. Pricing of options and other complex derivative

securities requires the use of continuously compounded interest rates. Most books on

derivatives use continuous compounding for pricing futures too. However, we have used


discrete compounding as it is more intuitive and simpler to work with. Had we to use the

concept of continuous compounding, the above equation would have been expressed as:

F= Se rT

Where:

r: Cost of financing (using continuously compounded interest rate)

T: Time till expiration

e: 2.71828

5.3.2 Pricing futures contracts on commodities

Let us take an example of a futures contract on a commodity and work out the price of

the contract. The spot price of silver is Rs.7000/kg. If the cost of financing is 15%

annually, what should be the futures price of 100 gms of silver one month down the line ?

Let us assume that we’re on 1st January 2001. How would we compute the price of a

silver futures contract expiring on 30th January? From the discussion above we know that

the futures price is nothing but the spot price plus the cost-of-carry. Let us first try to

work out the components of the cost-of-carry model.

1. What is the spot price of silver? The spot price of silver, S= Rs.7000/kg.

2. What is the cost of financing for a month? (1+0.15) 30/365

3. What are the holding costs? Let us assume that the storage cost = 0.

In this case the fair value of the futures price, works out to be = Rs.708.

F=s (1+r) T + C = 700(1.15) 30/365 =Rs. 708

If the contract was for 3 month period i.e. expiring 30th March the cost of financing would

increase the futures price. Therefore, the futures price would be C = 700(1.15) 90/365 =

Rs.724.5. On the other hand, if the one-month contract was for 10,000 kg. Of silver

instead of 100 gms, then it would involve a non-zero storage cost, and the price of the

future contract would be Rs. 708 +the cost of storage.

5.3.3 Pricing futures contracts on equity index

A futures contract on the stock market index gives its owner the right and obligation to

buy or sell the portfolio of stocks characterized by the index. Stock index futures are cash

settled; there is no delivery of the underlying stocks.


In their short history of trading, index futures have had a great impact on the world’s

securities markets. Indeed, index futures trading has been accused of making the world’s

stock markets more volatile than ever before. The critics claim that individual investors

have been driven out to the equity markets because the actions of institutional traders in

both the spot and futures markets cause stock values to gyrate with no links to their

fundamental values. Whether stock index futures trading is a blessing or a curse is

debatable. It is certainly true, however, that its existence has revolutionized the art and

science of institutional equity portfolio management.

The main differences between commodity and equity index futures are that: _

There are no costs of storage involved in holding equity.

Equity comes with a dividend stream, which is a negative cost if you are long the

stock and a positive cost if you are short the stock.

Therefore, Cost of carry = Financing cost - Dividends

Thus, a crucial aspect of dealing with equity futures as opposed to commodity futures is

an accurate forecasting of dividends. The better the forecast of dividend offered by a

security, the better is the estimate of the futures price.

5.3.4 Pricing index futures given expected dividend amount

The pricing of index futures is also based on the cost-of-carry model, where the carrying

cost is the cost of financing the purchase of the portfolio underlying the index, minus the

present value of dividends obtained from the stocks in the index portfolio.

Example

Nifty futures trade on NSE as one,two and three-month contracts. What will be the price

of a new two-month futures contract on Nifty?

1. Let us assume that M & M will be declaring a dividend of Rs. 10 per share after 15

days of purchasing the contract.

2. Current value of Nifty is 1200 and Nifty trades with a multiplier of 200.

3. Since Nifty is traded in multiples of 200, value of the contract is 200*1200 =

Rs.240,000.


4. If M & M has a weight of 7% in Nifty, its value in Nifty is Rs.16,800 i.e.(240,000 *

0.07).

5. If the market price of M & M is Rs.140, then a traded unit of Nifty involves 120 shares

of M & M i.e.(16,800/140).

6. To calculate the futures price, we need to reduce the cost-of-carry to the extent of

dividend received. The amount of dividend received is Rs.1200 i.e.(120 * 10). The

dividend is received 15 days later and hence compounded only for the remainder of 45

days. To calculate the futures price we need to compute the amount of dividend received

per unit of Nifty. Hence we divide the compounded dividend figure by 200.

7. Thus, futures price F = 1200(1.15) 60/365 {120*10(1.15) 45/365 /200} =Rs. 1221.80

5.3.5 Pricing index futures given expected dividend yield

If the dividend flow throughout the year is generally uniform, i.e. if there are few

historical cases of clustering of dividends in any particular month, it is useful to calculate

the annual dividend yield.

F = s (1+r-q) T

Where:

F: futures price

S: spot index value

r: cost of financing

q: expected dividend yield

T: holding period

Example

A two-month futures contract trades on the NSE. The annual dividend yield on Nifty is

2% annualized. The spot value of Nifty 1200. What is the fair value of the futures

contract?

Fair value = 1200(1+.015-0.02) 60/365 =Rs. 1224.35

The cost of carry model explicitly defines the relationship between the futures price and

the related spot price. As we know, the difference between the futures price and the spot

price is called the basis.


Nuances

As the date of expiration comes near, the basis reduces - there is a convergence of the

futures price towards the spot price. On the date of expiration, the basis is zero. If it is

not, then there is an arbitrage opportunity. Arbitrage opportunities can also arise when

the basis (difference between spot and futures price) or the spreads (difference

between prices of two futures contracts) during the life of a contract are incorrect. At

a later stage we shall look at how these arbitrage opportunities can be exploited.

There is nothing but cost-of-carry related arbitrage that drives the behavior of the

futures price.

Transactions costs are very important in the business of arbitrage.

Note: The pricing models discussed in this chapter give an approximate idea about the

true future price. However the price observed in the market is the outcome of the price–

discovery mechanism (demand–supply principle) and may differ from the so-called true

price.

5.4 Pricing options

An option buyer has the right but not the obligation to exercise on the seller. The worst

that can happen to a buyer is the loss of the premium paid by him. His downside is

limited to this premium, but his upside is potentially unlimited. This optionality is

precious and has a value, which is expressed in terms of the option price. Just like in

other free markets, it is the supply and demand in the secondary market that drives the

rice of an option. On dates prior to 31 Dec 2000, the “call option on Nifty expiring on 31

Dec 2000 with a strike of 1500” will trade at a price that purely reflects supply and

demand. There is a separate order book for each option which generates its own price.

The values shown in Table 5.1 are derived from a theoretical model, namely the Black-

Scholes option pricing model. If the secondary market prices deviate from these values, it

would imply the presence of arbitrage opportunities, which (we might expect) would be

swiftly exploited. But there is nothing innate in the market, which forces the prices in the

table to come about.


There are various models, which help us get close to the true price of an option. Most of

these are variants of the celebrated Black-Scholes model for pricing European options.

Today most calculators and spreadsheets come with a built-in Black-Scholes options

pricing formula so to price options we don’t really need to memorize the formula. What

we shall do here is discuss this model in a fairly non-technical way by focusing on the

basic principles and the underlying intuition.

5.5 Introduction to the Black–Scholes formulae

Intuition would tell us that the spot price of the underlying, exercise price, risk-free

interest rate, volatility of the underlying, time to expiration and dividends on the

underlying (stock or index) should affect the option price. Interestingly before Black and

Scholes came up with their option pricing model, there was a widespread belief that the

expected growth of the underlying ought to affect the option price. Black and Scholes

demonstrate that this is not true. The beauty of the Black and Scholes model is that like

any good model, it tells us what is important and what is not. It doesn’t promise to

Table 5.1 Option prices: some illustrative values

Option strike price

1400 1450 1500 1550 1600

Calls

1 mth 117 79 48 27 13

3 mth 154 119 90 67 48

Puts

1 mth 8 19 38 66 102

3 mth 25 39 59 84 114

Assumptions: Nifty spot is 1500, Nifty volatility is 25% annualized, interest rate is 10%,

and Nifty dividend yield is 1.5%.

produce the exact prices that show up in the market, but definitely does a remarkable job

of pricing options within the framework of assumptions of the model. Virtually all option


pricing models, even the most complex ones, have much in common with the Black–

Scholes model.

Black and Scholes start by specifying a simple and well–known equation that models the

way in which stock prices fluctuate. This equation called Geometric Brownian Motion,

implies that stock returns will have a lognormal distribution, meaning that the logarithm

of the stock’s re-turn will follow the normal (bell shaped) distribution. Black and Scholes

then propose that the option’s price is determined by only two variables that are allowed

to change: time and the underlying stock price. The other factors - the volatility, the

exercise price, and the risk–free rate do affect the option’s price but they are not allowed

to change. By forming a portfolio consisting of a long position in stock and a short

position in calls, the risk of the stock is eliminated. This hedged portfolio is obtained by

setting the number of shares of stock equal to the approximate change in the call price for

a change in the stock price. This mix of stock and calls must be revised continuously, a

process known as delta hedging.

Black and Scholes then turn to a little–known result in a specialized field of probability

known as stochastic calculus. This result defines how the option price changes in terms of

the change in the stock price and time to expiration. They then reason that this hedged

combination of options and stock should grow in value at the risk–free rate. The result

then is a partial differential equation. The solution is found by forcing a condition called a

boundary condition on the model that requires the option price to converge to the exercise

value at expiration. The end result is the Black and Scholes model.

5.6 The Black–Scholes option pricing formulae

The Black–Scholes formulas for the prices of European calls and puts on a non-dividend

paying stock are:

C = SN(d1) – Xe-rT N(d2)

P = Xe-rT N(-d2)- SN(-d1)

Where d1 = [ ln s/x +(r+δ2/2)T ]/ δ √T


And d2 = d1 –δ√T

The Black Scholes equation is done in continuous time. This requires continuous

compounding. The “ r ” that in this is ln(1+r). E.g. if the interest rate per annum is

12%, you need to use ln1.12 or 0.1133, which is continuously compounded

equivalent of 12% per annum.

N () is the cumulative normal distribution. N(d1 ) is called the delta of the option

which is a measure of change in option in option price with respect to change in the

price of the underlying asset.

δ a measure of volatility is the annualized standard deviation of continuously

compounded returns on the underlying. When daily sigma are given, they need to be

converted into annualized sigma.

Σ annual = Σ daily * √number of trading days per year. On a average there are 250 trading

days in a year.

X is the exercise price, S is the spot price and T the time to expiration.

5.7 Pricing index options

Under the assumptions of the Black–Scholes options pricing model, index options should

be valued in the same way as ordinary options on common stock. The assumption is that

investors can costlessly purchase the underlying stocks in the exact amount necessary to

replicate the index; that is, stocks are infinitely divisible and that the index follows a

diffusion process such that the continuously compounded returns distribution of the index

is normally distributed. To use the Black–Scholes formula for index options, we must

however make adjustments for the dividend payments received on the index stocks. If the

dividend payment is sufficiently smooth, this merely involves replacing the current index

value S in the model with Se-qT where q is the annual dividend yield and T is the time to

expiration in years.

The Black-Scholes formula is so commonly used that it comes programmed into most

calculators and spreadsheets. Hence it is not necessary to memorize the formula. One

only needs to know how to use it.


Note: The pricing models discussed in this chapter give an approximate idea about the

true options price. However the price observed in the market is the outcome of the price–

discovery mechanism (demand–supply principle) and may differ from the so-called true

price.


6.0Using index futuresThere are eight basic modes of trading on the index futures market:13

13 Source: NSE Derivatives Module & www.rediff/money/derivatives.htm & www.erivativesreview.com


Hedging

H1 Long stock, short Nifty futures

H2 Short stock, long Nifty futures

H3 Have portfolio, short Nifty futures

H4 Have funds, long Nifty futures

Speculation

S1 Bullish index, long Nifty futures

S2 Bearish index, short Nifty futures

Arbitrage

A1 Have funds, lend them to the market

A2 Have securities, lend them to the market

6.1 H1: Long stock, short Nifty futures

Have you ever felt that a stock was intrinsically undervalued? That the profits and the

quality of the company made it worth a lot more as compared with what the market

thinks? Have you ever been a “stockpicker” and carefully purchased a stock based on a

sense that it was worth more than the market price?

A person who feels like this takes a long position on the cash market. When doing this,

he faces two kinds of risks:

1. His understanding can be wrong, and the company is really not worth more than the

market price; or,

2. The entire market moves against him and generates losses even though the underlying

idea was correct.

The second outcome happens all the time. A person may buy Infosys at Rs.190 thinking

that it would announce good results and the stock price would rise. A few days later, Nifty

drops, so he makes losses, even if his understanding of Infosys was correct.


There is a peculiar problem here. Every buy position on a stock is simultaneously a buy

position on Nifty. This is because a LONG INFOSYS position generally gains if Nifty

rises and generally loses if Nifty drops. The stock picker may be thinking he wants to be

LONG INFOSYS, but a long position on Reliance effectively forces him to be LONG

INFOSYS + LONG NIFTY.

It is useful to ask: does the person feel bullish about INFOSYS or about the index?

Those who are bullish about the index should just buy Nifty futures; they need not

trade individual stocks.

Those who are bullish about INFOSYS do wrong by carrying along a long position

on Nifty as well.

There is a simple way out. Every time you adopt a long position on a stock, you should

sell some amount of Nifty futures. This offsets the hidden Nifty exposure that is inside

every long–stock position. Once this is done, you will have a position, which is purely

about the performance of the stock. The position LONG INFOSYS + SHORT NIFTY is

a pure play on the value of INFOSYS, without any extra risk from fluctuations of the

market index. When this is done, the stockpicker has “hedged away” his index exposure.

Warning: Hedging does not remove losses. The best that can be achieved using hedging

is the removal of unwanted exposure, i.e. unnecessary risk. The hedged position will

make less profits than the un-hedged position, half the time. One should not enter into a

hedging strategy hoping to make excess profits for sure; all that can come out of hedging

is reduced risk.

How do we actually do this?

1. We need to know the “beta” of the stock, i.e. the average impact of a 1% move in Nifty

upon the stock. If betas are not known, it is generally safe to assume the beta is 1.

Suppose we take WIPRO, whose beta is 1.2, and suppose we have a LONG WIPRO

position of Rs.200,000.

2. The size of the position that we need on the index futures market, to completely

remove the hidden Nifty exposure, is 1.2 *œ200,000, i.e. Rs.240,000.

3. Suppose Nifty is at 1200, and the market lot on the futures market is 200. Hence each

market lot of Nifty is Rs.240,000. To sell Rs.240,000 of Nifty we need to sell one market

lot.


4. We sell one market lot of Nifty (200 nifties) to get the position:

LONG WIPRO Rs.200,000, SHORT WIPRO Rs.240,000

This position will be essentially immune to fluctuations of Nifty. The profits/losses

position will fully reflect price changes intrinsic to WIPRO, hence only successful

forecasts about WIPRO will benefit from this position. Returns on the position will be

roughly neutral to movements of Nifty.

6.2 H2: Short stock, long Nifty futures

Have you ever felt that a stock was intrinsically over-valued? That the profits and the

quality of the company made it worth a lot less as compared to what the market thinks?

Have you ever been a “stockpicker” and carefully sold a stock based on a sense that it

was worth less than the market price?

A person who feels like this takes a short position on the cash market. While doing this,

he faces two kinds of risks:

1. His understanding can be wrong, and the company is really worth more than the

market price; or,

2. The entire market moves against him and generates losses even though the underlying

idea was correct.

The second outcome happens all the time. A person may sell Reliance at Rs.190 thinking

that Reliance would announce poor results and the stock price would fall. A few days

later, Nifty rises, so he makes losses, even if his intrinsic understanding of Reliance was

correct.

There is a peculiar problem here. Every sell position on a stock is simultaneously a sell

position on Nifty. This is because a SHORT RELIANCE position generally gains if Nifty falls

and generally loses if Nifty rises. In this sense, a SHORT RELIANCE position is not a

focused play on the valuation of Reliance. It carries a SHORT NIFTY position along with it,

as incidental baggage. The stockpicker may be thinking he wants to be SHORT RELIANCE,

but a short position on Reliance on the market effectively forces him to be SHORT

RELIANCE + SHORT NIFTY.

Those who are bearish about the index should just sell nifty futures; they need not

trade individual stocks.


Those who are bearish about RELIANCE do wrong by carrying along a short position

on Nifty as well.

There is a simple way out. Every time you adopt a short position on a stock, you should

buy some amount of Nifty futures. This offsets the hidden Nifty exposure that is inside

every short–stock position. Once this is done, you will have a position which is purely

about the performance of the stock. The position SHORT RELIANCE + LONG NIFTY is a pure

play on the value of RELIANCE, without any extra risk from fluctuations of the market

index.


1. We need to know the “beta” of the stock, i.e. the average impact of a 1% move in Nifty

upon the stock. If betas are not known, it is generally safe to assume the beta is 1.

Suppose we take WIPRO, where the beta is 1.2, and suppose we have a SHORT WIPRO

position of Rs.200,000.

2. The size of the position that we need on the index futures market, to completely

remove the hidden Nifty exposure, is 1.2 *¨ 200,000, i.e. Rs.240,000.

3. Suppose Nifty is at 1200, and the market lot on the futures market is 200. Hence each

market lot of Nifty is Rs.240,000. To long Rs.240,000 of Nifty we need to buy one

market lot.

4. We buy one market lot of Nifty (200 nifties) to get the position:

SHORT WIPRO Rs.200, 000, LONG NIFTY Rs.240,000

This position will be essentially immune to fluctuations of Nifty. The profits/losses

position will fully reflect price changes intrinsic to WIPRO, hence only successful

forecasts about WIPRO will benefit from this position. Returns on the position will be

roughly neutral to movements of Nifty.

6.3 H3: Have portfolio, short Nifty futures

Have you ever experienced the feeling of owning an equity portfolio, and then, one day,

becoming uncomfortable about the overall stock market? Sometimes, you may have a

view that stock prices will fall in the near future. At other times, you may see that the

market is in for a few days or weeks of massive volatility, and you do not have an


appetite for this kind of volatility. The union budget is a common and reliable source of

such volatility: market volatility is always enhanced for one week before and two weeks

after a budget. Many investors simply do not want the fluctuations of these three weeks.

This is particularly a problem if you expect to need to sell shares in the near future, for

example, in order to finance a purchase of a house. This planning can go wrong if by the

time you sell shares, Nifty has dropped sharply.

When you have such anxieties, there are two alternatives:

1 Sell shares immediately. This sentiment generates “panic selling” which is rarely

optimal for the investor.

2 Do nothing, i.e. suffer the pain of the volatility. This leads to political pressures for

government to “do something” when stock prices fall.

In addition, with the index futures market, a third and remarkable alternative becomes

available:

3 Remove your exposure to index fluctuations temporarily using index futures. This

allows rapid response to market conditions, without “panic selling” of shares. It allows an

investor to be in control of his risk, instead of doing nothing and suffering the risk.

The idea here is quite simple. Every portfolio contains a hidden index exposure. This

statement is true for all portfolios, whether a portfolio is composed of index stocks or not.

In the case of portfolios, most of the portfolio risk is accounted for by index fluctuations

(unlike individual stocks, where only 30–60% of the stock risk is accounted for by index

fluctuations). Hence a position LONG PORTFOLIO + SHORT NIFTY can often become one–

tenth as risky as the LONG PORTFOLIO position!

Suppose we have a portfolio of Rs.1 million which has a beta of 1.25. Then a complete

hedge is obtained by selling Rs.1.25 million of Nifty futures.

Warning: Hedging does not always make money. The best that can be achieved using

hedging is the removal of unwanted exposure, i.e. unnecessary risk. The hedged position

will make less profit than the unhedged position, half the time. One should not enter into


a hedging strategy hoping to make excess profits for sure; all that can come out of

hedging is reduced risk.

The investor should adopt this strategy for the short periods of time where (a) the market

volatility that he anticipates makes him uncomfortable, or (b) when his financial planning

involves selling shares at a future date and would be affected if Nifty drops. It does not

make sense to use this strategy for long periods of time – if a two–year hedging is

desired, it is better to sell the shares, invest the proceeds, and buy back shares after two

years. This strategy makes the most sense for rapid adjustments.

Another important choice for the investor is the degree of hedging. Complete hedging

eliminates all risk of gain or loss. Sometimes the investor may be willing to tolerate some

risk of loss so as to hang on to some risk of gain. In that case, partial hedging is

appropriate. The complete hedge may require selling Rs.3 million of the futures, but the

investor may choose to only sell Rs.2 million of the futures. In this case, two–thirds of his

portfolio is hedged and one–third ofthe portfolio is held unhedged. The exact degree of

hedging chosen depends upon the appetite for risk that the investor has.

6.4 H4: Have funds, buy Nifty futures

Have you ever been in a situation where you had funds which needed to get invested in

equity? Or of expecting to obtain funds in the future which will get invested in equity.

Some common occurrences of this include:

A closed-end fund which just finished its initial public offering has cash which is not

yet invested.

Suppose a person plans to sell land and buy shares. The land deal is slow and takes

weeks to complete. It takes several weeks from the date that it becomes sure that the

funds will come to the date that the funds actually are in hand.

An open-ended fund has just sold fresh units and has received funds.

Getting invested in equity ought to be easy but there are three problems:

1. A person may need time to research stocks, and carefully pick stocks that are expected

to do well. This process takes time. For that time, the investor is partly invested in cash


and partly invested in stocks. During this time, he is exposed to the risk of missing out if

the overall market index goes up.

2. A person may have made up his mind on what portfolio he seeks to buy, but going to

the market and placing market orders would generate large ‘impact costs’. The execution

would be improved substantially if he could instead place limit orders and gradually

accumulate the portfolio at favor-able prices. This takes time, and during this time, he is

exposed to the risk of missing out if the Nifty goes up.

3. In some cases, such as the land sale above, the person may simply not have cash to

immediately buy shares, hence he is forced to wait even if he feels that Nifty is unusually

cheap. He is exposed to the risk of missing out if Nifty rises.

So far, in India, we have had exactly two alternative strategies which an investor can

adopt: to buy liquid stocks in a hurry, or to suffer the risk of staying in cash. With Nifty

futures, a third alternative becomes available:

The investor would obtain the desired equity exposure by buying index futures,

immediately. A person who expects to obtain Rs.5 million by selling land would

immediately enter into a position LONG NIFTY worth Rs.5 million. Similarly, a

closed end fund which has just finished its initial public offering and has cash which

is not yet invested, can immediately enter into a LONG NIFTY to the extent it wants

to be invested in equity. The index futures market is likely to be more liquid than

individual stocks so it is possible to take extremely large positions at a low impact

cost.

Later, the investor/closed-end fund can gradually acquire stocks (either based on

detailed research and/or based on aggressive limit orders). As and when shares are

obtained, one would scale down the LONG NIFTY position correspondingly. No

matter how slowly stocks are purchased, this strategy would fully capture a rise in

Nifty, so there is no risk of missing out on a broad rise in the stock market while this

process is taking place. Hence, this strategy allows the investor to take more care and

spend more time in choosing stocks and placing aggressive limit orders.


Hedging is often thought of as a technique that is used in the context of equity exposure.

It is common for people to think that the owner of shares needs index futures to hedge

against a drop in Nifty. Holding money in hand, when you want to be invested in shares,

is a risk because Nifty may rise. Hence it is equally important for the owner of money to

use index futures to hedge against a rise in Nifty!

Table 6.1 Gradual acquisition of stocks, hedged

On 17 Feb, Iqbal purchased 5000 nifties to obtain a position of Rs.5 million. From 18 Feb

onwards, on each day, Iqbal purchased one security worth Rs.357,000 (at 17 Feb prices)

and sold off a similar value of futures thus shrinking his futures position. For this

example, we deliberately use non–index small stocks; hedging using index futures works

for all portfolios regardless of what stocks go into them. Nifty rose sharply on 27

February and 28 February, so his outstanding futures position generated an infusion of

cash for him on these days. This inflow paid for the higher stock prices that he suffered.

Date Futures position Stock purchase Futur

es

sold

MTM

profit/loss

(In Rs.)

17 Feb +5,000,000

18 Feb 4,597,074 2700 shares of ASIANHOTL 400 -17,042

19 Feb 4,190,807 2800 shares of BATAINDIA 400 38,430

20 Feb 3,786,330 5400 shares of BOMDYEING 400 18,801

23 Feb 3,375,976 55500 shares of SAIL 400 55,828

24 Feb 2,964,000 6050 shares of ESCORTS 400 13,795

25 Feb 2,648,488 1600 shares of DABUR 300 65,300

26 Feb 2,330,165 500 shares of CIPLA 300 25,290

27 Feb 2,007,454 1150 shares of CADBURY 300 35,112

02 Mar 1,673,850 4700 shares of APOLLOTYRE 300 76,248

03 Mar 1,350,948 5100 shares of ICICIBK 300 -64,214

04 Mar 1,019,453 2150 shares of ITCHOTEL 300 42,968


05 Mar 690,853 2100 shares of LAKME 300 -11,582

06 Mar 362,993 700 shares of PFIZER 300 -2,220

09 Mar 29,828 6300 shares of TITAN 300 10,611

Total 4,982,538 249,724


1. Mr.Mehta obtained Rs.5 million on 17 Feb 1998. He made a list of 14 stocks to buy, at

17 Feb prices, totaling Rs.5 million.

2. At that time Nifty was at 991.70. He entered into a LONG NIFTY MARCH

FUTURES position for 5000 nifties, i.e. his long position was worth 5,053,600.

3. From 18 Feb 1998 to 09 March 1998 he gradually acquired the stocks (see Table 5.2).

On each day, he purchased one stock and sold off a corresponding amount of futures.

On each day, the stocks purchased were at a changed price (as compared to the price

prevalent on 17 Feb). On each day, he obtained or paid the ‘mark–to–market margin’ on

his outstanding futures position, thus capturing the gains on the index.

4. By 09 Mar 1998 he had fully invested in all the shares that he wanted (as of 17 Feb)

and had no futures position left.

5. The same sequencing of purchases, without the umbrella of protection of the LONG

NIFTY MARCH FUTURES position, would have cost Rs.249,724 more.

6.5 S1: Bullish index, long Nifty futures

Do you sometimes think that the market index is going to rise? That you could make a

profit by adopting a position on the index? How does one implement a trading strategy to

benefit from an upward movement in the index? Today, you have two choices:

1. Buy selected liquid securities, which move with the index, and sell them at a later date:

or, 2. Buy the entire index portfolio and then sell it at a later date.

The first alternative is widely used – a lot of the trading volume on liquid stocks is based

on using these liquid stocks as an index proxy. However, these positions run the risk of


making losses owing to company–specific news; they are not purely focused upon the

index. The second alternative is cumbersome and expensive in terms of transactions

costs.


When you think the index will go up, buy the Nifty futures. The minimum market lot is

200 Nifties. Hence, if Nifty is at 1200, the investment is done in units of Rs.240,000.

When the trade takes place, the investor is only required to pay up the initial margin,

which is something like Rs.20,000. Hence, by paying an initial margin of Rs.20,000, the

investor gets a claim on the index worth Rs.240,000. Similarly, by paying up Rs.200,000,

the investor gets a claim on Nifty worth Rs.2.4 million.

Futures are available at several different expirations. The investor can choose any of them

to implement this position. The choice is basically about the horizon of the investor.

Longer dated futures go well with long–term forecasts about the movement of the index.

Shorter dated futures tend to be more liquid.

6.6 S2: Bearish index, short Nifty futures

Do you sometimes think that the market index is going to fall? That you could make a


benefit from a downward movement in the index? Today, you have two choices:

1. Sell selected liquid securities which move with the index, and buy them at a later date:

or, 2. Sell the entire index portfolio and then buy it at a later date.

The first alternative is widely used – a lot of the trading volume on liquid stocks is based

on using these stocks as an index proxy. However, these positions run the risk of making

losses owing to company–specific news; they are not purely focused upon the index.

The second alternative is hard to implement. This strategy is also cumbersome and

expensive in terms of transactions costs.



When you think the index will go down, sell the Nifty futures. The minimum market lot

is 200 Nifties. Hence, if Nifty is at 1200, the investment is done in units of Rs.240,000.

When the trade takes place, the investor is only required to pay up the initial margin,

which is something like Rs.20,000. Hence, by paying an initial margin of Rs.20,000 the

investor gets a claim on the index worth Rs.240,000. Similarly, by paying up Rs.200,000,

the investor gets a claim on Nifty worth Rs.2.4 million.

Futures are available at several different expirations. The investor can choose any of them

to implement this position. The choice is basically about the horizon of the investor.

Longer dated futures go well with long–term forecasts about the movement of the index.

Shorter dated futures tend to be more liquid.

6.7 A1: Have funds, lend them to the market

Would you like to lend funds into the stock market, without suffering the slightest risk?

Traditional methods of loaning money into the stock market suffer from (a) price risk of

shares and (b) credit risk of default of the counter-party. What is new about the index

futures market is that it supplies a technology to lend money into the market without

suffering any exposure to Nifty, and without bearing any credit risk.

The basic idea is simple. The lender buys all 50 stocks of Nifty on the cash market, and

simultaneously sells them at a future date on the futures market. It is like a repo. There is

no price risk since the position is perfectly hedged. There is no credit risk since the

counterparty on both legs is the NSCCL which supplies clearing services on NSE. It is an

ideal lending vehicle for entities which are shy of price risk and credit risk, such as

traditional banks and the most conservative corporate treasuries.


1. Calculate a portfolio which buys all the 50 stocks in Nifty in correct proportion, i.e.

where the money invested in each stock is proportional to its market capitalization.

2. Round off the number of shares in each stock.


3. Using the NEAT software, a single keystroke can fire off these 50 orders in rapid

succession into the NSE trading system. This gives you the buy position.

4. A moment later, sell Nifty futures of equal value. Now you are completely hedged, so

fluctuations in Nifty do not affect you.

5. A few days later, you will have to take delivery of the 50 stocks and pay for them. This

is the point at which you are “loaning money to the market”.

6. Some days later (anytime you want), you will unwind the entire transaction.

7. At this point, use NEAT to send 50 sell orders in rapid succession to sell off all the 50

stocks.

8. A moment later, reverse the futures position. Now your position is down to 0.

9. A few days later, you will have to make delivery of the 50 stocks and receive money

for them. This is the point at which “your money is repaid to you”.

What is the interest rate that you will receive? We will use one specific case, where you

will unwind the transaction on the expiration date of the futures. In this case, the

difference between the futures price and the cash Nifty is the return to the moneylender,

with two complications: the moneylender additionally earns any dividends that the 50

shares pay while he has held them, and the moneylender suffers transactions costs

(impact cost, brokerage) in doing these trades. On 1 July 1998, if the Nifty spot is 942.25,

and the Nifty July 1998 futures are at 956.5 then the difference (1.5% for 30 days) is the

return that the moneylender obtains.

Example

On 1 August, Nifty is at 1200. A futures contract is trading with 27 August expiration for

1230. Ashish wants to earn this return (30/1200 for 27 days).

1. He buys Rs.3 million of Nifty on the spot market. In doing this, he places 50 market

orders and ends up paying slightly more. His average cost of purchase is 0.3% higher, i.e.

he has obtained the Nifty spot for 1204.

2. He sells Rs.3 million of the futures at 1230. The futures market is extremely liquid so

the market order for Rs.3 million goes through at near–zero impact cost.

3. He takes delivery of the shares and waits.


4. While waiting, a few dividends come into his hands. The dividends work out to

Rs.7,000.

5. On 27 August, at 3:15, Ashish puts in market orders to sell off his Nifty portfolio,

putting 50 market orders to sell off all the shares. Nifty happens to have closed at 1210

and his sell orders (which suffer impact cost) goes through at 1207.

6. The futures position spontaneously expires on 27 August at 1210 (the value of the

futures on the last day is always equal to the Nifty spot).

7. Ashish has gained Rs.3 (0.25%) on the spot Nifty and Rs.20 (1.63%) on the futures for

a return of near 1.88%. In addition, he has gained Rs.70,000 or 0.23% owing to the

dividends for a total return of 2.11% for 27 days, risk free.

It is easier to make a rough calculation of the return. To do this, we ignore the gain from

dividends and we assume that transactions costs account for 0.4%. In the above case, the

return is roughly 1230/1200 or 2.5% for 27 days, and we subtract 0.4% for transactions

costs giving 2.1% for 27 days. This is very close to the actual number.

6.8 A2: Have securities, lend them to the market

Do you have a portfolio of shares which is earning you nothing? Would you like to juice

up your returns by earning revenues from stocklending?

Most owners of shares answer in the affirmative to these questions. Yet, stocklending

schemes that are widely accessible do not exist in India.

The index futures market offers a riskless mechanism for (effectively) loaning out shares

and earning a positive return for them. It is like a repo; you would sell off your

certificates and con-tract to buy them back in the future at a fixed price. There is no price

risk (since you are perfectly hedged) and there is no credit risk (since your counterparty

on both legs of the transaction is the NSCCL).

The basic idea is quite simple. You would sell off all 50 stocks in Nifty and buy them

back at a future date using the index futures. You would soon receive money for the


shares you have sold. You can deploy this money as you like until the futures expiration.

On this date, you would buy back your shares, and pay for them.


Suppose you have Rs.5 million of the NSE-50 portfolio (in their correct proportion, with

each share being present in the portfolio with a weight that is proportional to its market

capitalization).

1. Sell off all 50 shares on the cash market. This can be done using a single keystroke

using the NEAT software.

2. Buy index futures of an equal value at a future date.

3. A few days later, you will receive money and have to make delivery of the 50 shares.

4. Invest this money at the riskless interest rate.

5. On the date that the futures expire, at 3:15 PM, put in 50 orders (using NEAT again) to

buy the entire NSE-50 portfolio.

6. A few days later, you will need to pay in the money and get back your shares.

When is this worthwhile? When the spot-futures basis (the difference between spot Nifty

and the futures Nifty) is smaller than the riskless interest rate that you can find in the

economy. If the spot–futures basis is 2.5% per month and you are loaning out the money

at 1.5% per month, it is not profitable. Conversely, if the spot-futures basis is 1% per

month and you are loaning out money at 1.2% per month, this stocklending could be

profitable.

It is easy to approximate the return obtained in stock lending. To do this, we assume that

transactions costs account for 0.4%. Suppose the spot–futures basis is x% and suppose

the rate at which funds can be invested is y% Then the total return is y-x-0.4%, over the

time that the position is held.

This can also be interpreted as a mechanism to obtain a cash loan using your portfolio of

Nifty shares as collateral. In this case, it may be worth doing even if the spot–futures

basis is somewhat wider.

Example


Suppose the Nifty spot is 1100 and the two–month futures are trading at 1110. Hence the

spot– futures basis (1110/1100) is 0.9%. Suppose cash can be risklessly invested at 1%

per month. Over two months, funds invested at 1% per month yield 2.01%. Hence the

total return that can be obtained in stocklending is 2.01-0.9-0.4 or 0.71% over the two–

month period.

Let us make this concrete using a specific sequence of trades. Suppose Akash has Rs.4

million of the Nifty portfolio which he would like to lend to the market.

1. Akash puts in sell orders for Rs.4 million of Nifty using the feature in NEAT to rapidly

place 50 market orders in quick succession. The seller always suffers impact cost;

suppose he obtains an actual execution at 1098.

2. A moment later, Akash puts in a market order to buy Rs.4 million of the Nifty futures.

The order executes at 1110. At this point, he is completely hedged.

3. A few days later, Akash makes delivery of shares and receives Rs.3.99 million

(assuming an impact cost of 2/1100).

4. Suppose Akash lends this out at 1% per month for two months.

5. At the end of two months, he get back Rs.4,072,981. Translated in terms of Nifty, this

is 1098*1.012 or 1120.

6. On the expiration date of the futures, he puts in 50 orders, using NEAT, placing market

orders to buy back his Nifty portfolio. Suppose Nifty has moved up to 1150 by this time.

This makes shares are costlier in buying back, but the difference is exactly offset by

profits on the futures contract.

When the market order is placed, suppose he ends up paying 1153 and not 1150, owing to

impact cost. He has funds in hand of 1120, and the futures contract pays 40 (1150-1110)

so he ends up with a clean profit, on the entire transaction, of 1120 + 40 - 1153 or 7. On a

base of Rs.4 million, this is Rs.25, 400.

Table 6.2 Market watch showing bid and ask for various futures contracts

Month Quantity Bid Ask Quantity

November 1000 1009 1010.5 1000


December 200 1022 1025 400

7.0 Using index optionsThere are potentially innumerable ways of trading on the index options market. However

we shall look at eight basic modes of trading on the index futures market:

Hedging

H5 Have portfolio, buy puts

Speculation

S3 Bullish index, buy Nifty calls or sell Nifty puts

S4 Bearish index, sell Nifty calls or buy Nifty puts

S5 Anticipate volatility, buy a call and a put at same strike

S6 Bull spreads, Buy a call and sell another

S7 Bear spreads, Sell a call and buy another

Arbitrage

A3 Put-call parity with spot-options arbitrage

A4 Arbitrage beyond option price bounds14

7.1 H5: Have portfolio, buy puts

Have you ever experienced the feeling of owning an equity portfolio, and then, one day,

becoming uncomfortable about the overall stock market?

14 Source: NSE Derivatives Module, www.derivativesindia.com, www.erivativesreview.com, www.rediff/money/derivatives.htm


Sometimes you may have a view that stock prices will fall in the near future. Many

investors simply do not want the fluctuations of these three weeks. One way to protect

your portfolio from potential downside due to a market drop is to buy portfolio insurance.

Index options is a cheap and easily implementable way of seeking this insurance. The

idea is simple. To protect the value of your portfolio from falling below a particular level,

buy the right number of put options with the right strike price. When the index falls your

portfolio will lose value and the put options bought by you will gain, effectively ensuring

that the value of your portfolio does not fall below a particular level. This level depends

on the strike price of the options chosen by you.

Portfolio insurance using put options is of particular interest to Mutual funds who already

own well-diversified portfolios. By buying puts, the fund can limit its downside in case of

a market fall.


We need to know the “beta” of the portfolio. We look at two cases, case one where the

portfolio has a beta of 1 and case two where the portfolio beta is not equal to 1.

Portfolio insurance when portfolio beta is 1.0

1. Assume we have a well-diversified portfolio with a beta of 1.0, which we would like to

insure against a fall in the market.

2. Now we need to choose the strike at which we should buy puts. This is largely a

function of how safe we want to play. Assume that the spot Nifty is 1250 and you decide

to buy puts with a strike of 1125. This will insure your portfolio against an index fall

lower than 1125.

3. When the portfolio beta is one, the number of puts to buy is simply equal to the

portfolio value divided by the spot index.

Now let us look at the outcome. We have just bought two–month Nifty puts at a strike of

1125. This is designed to ensure that the value of our portfolio does not decline below

Rs.0.90 million. (For a portfolio with a beta of 1, a 10% fall in the index directly


translates into a 10% fall in the portfolio value). During the two–month period, suppose

the Nifty drops to 1080. This is a 13.6% fall in the index. The portfolio value too falls at

the same rate and declines to Rs.0.864 million. However the options provide a payoff of

(1125-1080)*4*200 which is equal to Rs.36,000. This is the amount needed to bring the

value of the portfolio back to Rs.0.90 million.

Portfolio insurance when portfolio beta is not 1.0

1. Assume we have a portfolio with beta equal to 1.2 which we would like to insure

against a fall in the market.

2. Now we need to choose the strike at which we should buy puts. This is largely a

function of how safe we want to play. Assume that the spot Nifty is 1200 and we decide

to buy puts with a strike of 1140. This will insure our portfolio against an index fall lower

than 1140.

3. For a portfolio with a non-unit beta, the number of puts to buy equals (portfolio value *

portfolio beta)/Index. Assume our portfolio is worth Rs.1 million with a beta of 1.2.

Hence the number of puts we need to buy to protect our portfolio from a downside is

(10,00,000 *1.2)/1200 which works out to 1000. At a market lot of 200, it means that we

will have to buy 5 market lots of two month puts with a strike of 1140.

Now let us look at the outcome. We have just bought two month Nifty puts at a strike of

1140. This is designed to ensure the value of our portfolio does not decline below Rs.0.94

million. (For a portfolio with a beta of 1.2, an index fall of 5% translates into a 6% fall in

the portfolio value). During the two-month period, suppose the Nifty drops to 1080. The

portfolio value has declined to Rs.0.88 million. (Again, for a portfolio with a beta of 1.2,

a 10% fall in the index translates into a 12% fall in the portfolio value). However the

options provide a payoff of (1140-1080)*5*200 which is equal to Rs.60,0000. This is the

amount needed to bring the value of the portfolio back to Rs.0.94 million.

7.2 S3: Bullish index, buy Nifty calls or sell Nifty puts

Do you sometimes think that the market index is going to rise? That you could make a


benefit from an upward movement in the index? Today, using options you have two

choices:


1. Buy call options on the index; or,

2. Sell put options on the index

We have already seen the payoff of a call option. The downside to the buyer of the call

option is limited to the option premium he pays for buying the option. His upside

however is potentially unlimited.

Having decided to buy a call, which one should you buy? Table 7.1 gives the premia for

one-month calls and puts with different strikes. Given that there are a number of one–

month calls trading, each with a different strike price, the obvious question is: which

strike should you choose? Let us take a look at call options with different strike prices.

Assume that the current index level is 1250, risk-free rate is 12% per year and index

volatility is 30%. The following options are available:

1. A one month call on the Nifty with a strike of 1200.





Which of these options you choose largely depends on how strongly you feel about the

likelihood of the upward movement in the market index, and how much you are willing

to lose should this upward movement not come about. There are five one–month calls

and five one–month puts trading in the market.

Table 7.1 One-month calls and puts trading at different strikes

The spot Nifty level is 1250. There are five one-month calls and five one-month puts

trading in the market. Figure 7.1 shows the payoffs from buying calls at different strikes.

Figure 7.2 shows the payoffs from writing puts at different strikes.

Nifty Strike price of option Call Premium (Rs.) Put Premium (Rs.)

1250 1200 80.10 18.15

1250 1225 63.65 26.50

1250 1250 49.45 37.00


1250 1275 37.50 49.80

1250 1300 27.50 64.80

As a person who wants to speculate on the hunch that the market index may rise, you can

also do so by selling or writing puts. As the writer of puts, you face a limited upside and

an unlimited downside.

Having decided to write a put, which one should you write? Given that there are a

number of one-month puts trading, each with a different strike price, the obvious question

is: which strike should you choose ? This largely depends on how strongly you feel about

the likelihood of the upward movement in the market index. In the example in Figure 7.2,

at a Nifty level of 1250, one option is in–the–money and one is out–of–the–money. As

expected, the in–the–money option fetches the highest premium of Rs.64.80 whereas the

out–of–the–money option has the lowest premium of Rs.18.15.

Figure 7.1 Payoff for buyer of call options at various strikesThe figure shows the profits/losses for a buyer of Nifty calls at various strikes. The in–the–money option with a strike of 1200 has the highest premium of Rs.80.10 whereas the out–of–the–money option with a strike of 1300 has the lowest premium of Rs.27.50.

Profit

1200 1250 1300 1280.10 1299.45 1327.50 Nifty 27.50

49.45

80.10

Loss

Figure 7.2 Payoff for writer of put options at various strikesThe figure shows the profits/losses for a writer of Nifty puts at various strikes. The in–the–money option with a strike of 1300 fetches the highest premium of Rs.64.80 whereas the out–of–the–money option with a strike of 1200 has the lowest premium of Rs.18.15.


Profit

64.80

37.00

18.15

1200 1250 1300 1981.85 1213 1235.20 Nifty

Loss

7.3 S4: Bearish index: sell Nifty calls or buy Nifty puts

Do you sometimes think that the market index is going to drop? That you could make a


benefit from a downward movement in the index? Today, using options, you have two

choices:

1. Sell call options on the index; or,

2. Buy put options on the index

We have already seen the payoff of a call option. The upside to the writer of the call

option is limited to the option premium he receives upright for writing the option. His

downside however is potentially unlimited. Having decided to write a call, which one

should you write? Table 7.2 gives the premiums for one month calls and puts with

different strikes. Given that there are a number of one-month calls trading, each with a

different strike price, the obvious question is: which strike should you choose ? Let us

take a look at call options with different strike prices. Assume that the current index level

is 1250, risk-free rate is 12% per year and index volatility is 30%. You could write the

following options :







Which of this options you write largely depends on how strongly you feel about the

likelihood of the downward movement in the market index and how much you are willing

to lose should this downward movement not come about.

Table 7.2 One month calls and puts trading at different strikes

The spot Nifty level is 1250. There are five one-month calls and five one-

month puts trading in the market. Figure 7.3 shows payoff for seller of

various calls at different strikes. Figure 7.4 shows the payoffs from buying

puts at different strikes.


1250 1200 80.10 18.15

1250 1225 63.65 26.50

1250 1250 49.45 37.00

1250 1275 37.50 49.80

1250 1300 27.50 64.80

As a person who wants to speculate on the hunch that the market index may fall, you can

also buy puts. As the buyer of puts you face an unlimited upside but a limited downside.

If the index does fall, you profit to the extent the index falls below the strike of the put

purchased by you. Having decided to buy a put, which one should you buy? Given that

there are a number of one-month puts trading, each with a different strike price, the

obvious question is: which strike should you choose? This largely depends on how

strongly you feel about the likelihood of the downward movement in the market index.

Figure 7.3 Payoff for seller of call option at various strikes

The figure shows the profits/losses for a seller of Nifty calls at various strike prices. The in–the–money option has the highest premium of Rs.80.10 whereas the at–the–money option has the lowest premium of Rs.27.50.


Profit 80.10

1327.5 49.45

27.50

1200 1250 1300 Nifty

Loss 1280.10 1299.45

Figure 7.4 Payoff for buyer of put options at various strikes

The figure shows the profits/losses for a buyer of Nifty puts at various strike prices. The in–the–money option has the highest premium of Rs.64.80 whereas the at–the–money option has the lowest premium of Rs.18.50.

Profit

1182.85 | 1213 235.20 | | 1200 1250 1300 Nifty 18.15

37.00

64.80

Loss

7.4 S5: Anticipate volatility; buy a call and a put

Do you sometimes think that the market index is going to go through large swings in a

given period, but have no opinion on the direction of the swing? This strategy is useful in

times of uncertainty (e.g. recently during the WTC attacks). How does one implement a


trading strategy to benefit from market volatility? Combinations of call and put options

provide an excellent way to trade on volatility. Here is what you would have to do:

1. Buy call options on the index at a strike K and maturity T, and

2. Buy put options on the index at the same strike K and of maturity T.

This combination of options is often referred to as a Straddle and is an appropriate

strategy for an investor who expects a large move in the index but does not know in

which direction the move will be.

Consider an investor who feels that the index which currently stands at 1252 could move

significantly in three months. The investor could create a straddle by buying both a put

and a call with a strike close to 1252 and an expiration date in three months. Suppose a

three month call at a strike of 1250 costs Rs.95.00 and a three month put at the same

strike cost Rs.57.00. To enter into this positions, the investor faces a cost of Rs.152.00. If

at the end of three months, the index remains at 1252, the strategy costs the investor

Rs.150. (An up-front payment of Rs.152, the put expires worthless and the call expires

worth Rs.2). If at expiration the index settles around 1252, the investor incurs losses.

However, if as expected by the investors, the index jumps or falls significantly, he profits.

For a straddle to be an effective strategy, the investor’s beliefs about the market

movement must be different from those of most other market participants. If the general

view is that there will be a large jump in the index, this will reflect in the prices of the

options.

Figure 7.5 Payoff for buyer of three-month call and put options at strikes of 1250

The figure shows the profits/losses for a combination of a long call and a long put at the same strike and expiration. The investor has bought both a call and a put on the Nifty index. If on the expiration date, the index closes between 1098 and 1402, he losses a maximum of Rs.152. If however, his expectation of high volatility does come true, his profits are potentially unlimited. If for instance the index jumps to 1420, he makes a neat profit of Rs.18 i.e. (1420-1250)-152. The effectiveness of this combination depends how different is the investors belief about market movement from that of most other participants. The higher the cost of setting up this combination, the more the index would have to move for it to be profitable.


Profit

1098 1193 1250 1345 1402 | | | | |

57.00

95.00

152.00

Loss

Table 7.3 Three-month calls and puts trading at different strikes

Given below are the three-month call and put option premia on the S&P CNX Nifty. An

investor who decides to play on the volatility of the market must decide at what strike to

generate the straddle. In this case he has three three-month option contracts to choose

from.


1248 1250 48 38.30

1248 1245 50.65 35.95

1248 1230 59.05 29.50

7.5 S6: Bull spreads - Buy a call and sell another

There are times when you think the market is going to rise over the next two months,

however in the event that the market does not rise, you would like to limit your downside.


One way you could do this is by entering into a spread. A spread trading strategy

involves taking a position in two or more options of the same type, that is, two or more

calls or two or more puts. A spread that is designed to profit if the price goes up is called

a bull spread.

The cost of the bull spread is the cost of the option that is purchased, less the cost of the

option that is sold. Table 7.4 gives the profit/loss incurred on a spread position as the

index changes.

Figure 7.6 shows the payoff from the bull spread.

Broadly, we can have three types of bull spreads:

1. Both calls initially out-of-the-money,

2. One call initially in-the-money and one call initially out-of-the-money, and

3. Both calls initially in-the-money.

The decision about which of the three spreads to undertake depends upon how much risk

the investor is willing to take. The most aggressive bull spreads are of type 1. They cost

very little to set up, but have a very small probability of giving a high payoff.

Table 7.4 Expiration day cash flows for a Bull spread using two-month calls

The table shows possible expiration day profit for a bull spread created by buying one market lot of calls at a strike of 1260 and selling a market lot of calls at a strike of 1350. The cost of setting up the spread is the call premium paid (Rs.76.50) minus the call premium received (Rs.37.85), which is Rs.38.65. This is the maximum loss that the position will make. On the other hand, the maximum profit on the spread is limited to Rs.51.35. Beyond an index level of 1350, any profits made on the long call position will be cancelled by losses made on the short call position, effectively limiting the profit on the combination.

Nifty Buy Jan 1260 Call

Sell Jan 1350 Call

Cash Flow Profit & Loss (Rs.)

1245 0 0 0 -38.951255 0 0 0 -38.651265 +5 0 5 -33.651275 +15 0 15 -23.6561285 +25 0 25 -13.651295 +35 0 35 -3.651305 +45 0 45 +6.351315 +55 0 55 +16.351325 +65 0 65 +26.351335 +75 0 75 +36.35


1345 +85 0 85 +46.351355 +95 -5 90 +51.351365 +105 -15 90 +51.35

Figure 7.6 Payoff for a bull spread created using call options

The figure shows the profits/losses for a bull spread.As the index moves above 1260, the position starts making profits (cutting losses) until the spot reaches 1350. Beyond 1350, the profits made on the long call position get offset by the losses made on the short call position and hence the maximum profit on this spread is made if the index on the expiration day closes at 1350. Hence the payoff on this spread lies between 38.85 to 51.35.

Profit

51.35

37.85

1260 1298.65 1336.50 1350 1387.85 | | | | | Loss

38.65

76.50

7.6 S7: Bear spreads - sell a call and buy another

There are times when you think the market is going to fall over the next two months,

however in the event that the market does not fall, you would like to limit your downside.

One way you could do this is by entering into a spread. A spread trading strategy

involves taking a position in two or more options of the same type, that is, two or more


calls or two or more puts. A spread that is designed to profit if the price goes down is

called a bear spread.

A bear spread created using calls involves initial cash inflow since the price of the call

sold is greater than the price of the call purchased. Table 7.5 gives the profit/loss incurred

on a spread position as the index changes. Figure 7.7 shows the payoff from the bull

spread.

Broadly we can have three types of bear spreads:

1. Both calls initially out-of-the-money,

2. One call initially in-the-money and one call initially out-of-the-money, and

3. Both calls initially in-the-money.

The decision about which of the three spreads to undertake depends upon how much risk

the investor is willing to take. The most aggressive bear spreads are of type 1. They cost

very little to set up, but have a very small probability of giving a high payoff. As we

move from type 1 to type 2 and from type 2 to type 3, the spreads become more

conservative and cost higher to set up. Bear spreads can also be created by buying a put

with a high strike price and selling a put with a low strike price.

Figure 7.7 Payoff for a bear spread created using call optionsThe figure shows the profits/losses for a bear spread. As can be seen, the payoff obtained is the sum of the payoffs of the two calls, one sold at Rs.76.50 and the other bought at Rs.37.85. The maximum gain from setting up the spread is Rs.38.65 which is the difference between the call premium received and the call premium paid. The upside on the position is limited to this amount. Hence the payoff on this spread lies between +38.85 to -51.35.

Profit

76.50

38.65


1260 1298.65 1336.50 1350 1387.85 | | | | |

37.85

51.35

Loss

Table 7.5 Expiration day cash flows for a Bear spread using two-month calls

The table shows possible expiration day profit for a bear spread created by selling one market lot of calls at

a strike of 1260 and buying a market lot of calls at a strike of 1350.

Nifty Buy Jan 1350 Call

Sell Jan 1260 Call

Cash Flow Profit & Loss (Rs.)

1245 0 0 0 +38.951255 0 0 0 +38.651265 0 -5 -5 +33.651275 0 -15 -15 +23.6561285 0 -25 -25 +13.651295 0 -35 -35 +3.651305 0 -45 -45 -6.351315 0 -55 -55 -16.351325 0 -65 -65 -26.351335 0 -75 -75 -36.351345 0 -85 -85 -46.351355 +5 -95 -90 -51.351365 +15 -105 -90 -51.35

7.7 A3: Put-call parity with spot-options arbitrage

Have you ever wondered how the put prices relate to the call prices? If you happen to

know the call price on an asset, would that help you to get some idea of the price of a put

on the same asset? Do put prices have anything at all to do with call prices? Of course,

they do. The put and the call prices are related by a condition called the put-call parity.

We shall see how.

Put-call parity


To get an intuitive understanding about the put-call parity, we could think of it in the

following way. I buy the asset on spot, paying S. I buy a put at X, paying P, so my

downside below X is taken care of (if S < X, I will exercise the put). I sell a call at X,

earning C, so if S > X, the call holder will exercise on me, so my upside beyond X is

gone. This gives me X on T with certainty. This means that the portfolio of S+P-C is

nothing but a zero-coupon bond which pays X on date T.

What happens if the above equation does not hold good ? It gives rise to arbitrage

opportunities. The put-call parity basically explains the relationship between put, call,

stock and bond prices.

It is expressed as:

S + P – C = X / (1+r) T

Where:

S: Current index level

X: Exercise price of option

T: Time to expiration

C: Price of call option

P: Price of put option

R: risk-free rate of interest

The above expression shows that the value of a European call with a certain exercise

price and exercise date can be deduced from the value of a European put with the same

exercise price and date and vice versa. It basically means that the payoff from holding a

call plus an amount of cash equal to X / (1+r) T is the same as that of holding a put option

plus the index.

Case 1

Suppose Nifty stands at 1265, the risk-free rate of interest is 12% per annum, the price of

a three month Nifty 1260 call is Rs.96.50 and the price of a three month Nifty 1260 put is

Rs.60. In this case we can see that

S + P – C (not equal to) X / (1+r) T


1325 > 1321.30

What does this mean? If we think of index plus put as portfolio A and the call plus cash

as portfolio B, clearly portfolio A is overpriced relative to portfolio B. What would be the

arbitrage strategy in this case? Sell the securities in portfolio A and buy those in portfolio

B. This involves shorting the index and a put on the index and buying a call. How would

one short the index? One way to do it would be to actually sell off all 50 Nifty stocks in

the proportions in which they exist in the index. Another easier way to do this would be

to sell units of Index funds instead of the actual index stocks. This would achieve a

similar outcome. This entire set of transactions generates an up-front cash-flow of (1265

+ 60 - 96.50) = Rs.1228.50. When invested at the riskfree rate of 12%, this amount grows

to Rs.1265.35.

At expiration, if the index is higher than 1260, you will exercise the call. If the index is

lower than 1260, the buyer of the put will exercise on you. In either case, the investor

ends up buying the index at Rs.1260. Hence the net profit on the entire transaction is

Rs.5.35 (i.e. 1265.35-1260).


1. Sell off all 50 index shares on the cash market in the proportion in which they exist in

the index. This can be done using a single keystroke using the NEAT software.

2. Sell a three month Nifty 1260 put.

3. Buy a three month Nifty 1260 call.

4. You will receive the money for the stocks and the put sold and have to make delivery

of the 50

shares.

5. Invest this money at the riskless interest rate. In three months Rs.1228.50 will grow to

Rs.1265.35.

6. On the exercise date at 3:15 PM, if the Nifty is above 1260, exercise the call. If the

Nifty is below 1260, the put will be exercised on you.

7. Either way, you end up buying the index at Rs.1260.

8. The riskless profit on the transaction works out to be Rs.5.35.


Case 2:

Suppose Nifty stands at 1265, the risk-free rate of interest is 12% per annum, the price of

a three month Nifty 1260 call is Rs.96 and the price of a three month Nifty 1260 put is

51.50. In this case, we can see that

S + P – C (not equal to) X / (1+r) T

1316.50 < 1320.80

What does this mean? If we think of index plus put as portfolio A and the call plus cash

as portfolio B, clearly portfolio B is overpriced relative to portfolio A. What would be the

arbitrage strategy in this case? Buy the securities in portfolio A and sell those in portfolio

B. This involves buying the index and a put on the index and selling a call. How would

one buy the index? One way to do it would be to actually buy all 50 Nifty stocks in the

proportions in which they exist in the index. An easier way to do this would be to buy

units of Index funds instead of the actual index stocks. This would achieve a similar

outcome. This entire set of transactions involves an initial investment of Rs.1220.50(i.e.

1265 - 51.50 + 96) When financed at the riskfree rate of 12%, the repayment required at

the end of three months is Rs.1257.

At expiration if the index is lower than 1260, you will exercise the put. If the index is

higher than 1260, the buyer of the call will exercise on you. In either case, the investor

ends up buying the index at Rs.1260. Hence the net profit on the entire transaction is Rs.3

(1260 - 1257).


1. Buy all 50 index shares on the cash market in the proportion in which they exist in the

index. This can be done using a single keystroke using the NEAT software.

2. Buy a three month Nifty 1260 put.

3. Sell a three month Nifty 1260 call.

4. You will have to pay for the shares and the put, and will receive the call premium. The

entire set of transactions will require an initial outflow of Rs.1221.20.

5. Finance this money at the riskless interest rate. The repayment at the end of three

months works out to Rs.1257.


6. On the exercise date at 3:15 PM, if the Nifty is below 1260, exercise the put. If the

Nifty is above 1260, the call will be exercised on you.

7. Either way, you end up selling the index at Rs.1260.

8. The riskless profit on the transaction works out to be Rs.3.

7.8 A4: Arbitrage beyond option price bounds

The value of an option before expiration depends on six factors:¦

The level of the underlying index¦

The exercise price of the option¦

The time to expiration¦

The volatility of the index

The risk-free rate of interest

¦

Dividends expected during the life of the option

These factors set general boundaries for possible option prices. If the option price is

above the upper bound or below the lower bound, there are profitable arbitrage

opportunities. We shall try to get an intuitive understanding about these bounds.

Upper bounds for calls and puts

A call option gives the holder the right to buy the index for a certain price. No matter

what happens, the option can never be worth more than the index. Hence the index level

is an upper bound to the option price.

C (less than equal to) I

If this relationship is not true, an arbitrageur can easily make a riskless profit by buying

the index and selling the call option.

As we know a put option gives the holder the right to sell the index for X. No matter how

low the index becomes, the option can never be worth more than X. Hence,

P (less than equal to) X

If this is not true, an arbitrageur would make profit by writing puts.


Lower bounds for calls and puts

The lower bound for the price of a call option is given by S-X (1+r) –T The price of a call

must be worth at least this much else, it will be possible to make risk less profit

S-X (1+r) –T < C

Consider an example. Suppose the exercise price for a three-month Nifty call option is

1260. The spot index stands at 1386 and the risk-free rate of interest is 12% per annum.

In this case, he lower bound for the option price is 1386-1260 (1+1.2) –0.25 i.e. 161.20

Suppose the call is available at a premium of Rs.150 which is less than the theoretical

minimum of Rs. 163.20. An arbitrageur can buy a call and short the index. This provides

a cashflow of 1386-150 = 1236. If invested for three months at 12% per annum, the

Rs.1236 grows to Rs.1273. At the end of three months, the option expires. At this point,

the following could happen:

1. The index is above 1260, in which case the arbitrageur exercises his option and buys

back the index at 1260 making a profit of Rs.1273 - 1260 = Rs.13.

2. The index is below 1260 at say 1235, in which case the arbitrageur buys back the index

at the market price. He makes an even greater profit of 1273 - 1235 = Rs.38.

The lower bound for the price of a put option is given by X (1+r) -T –S. The price of a put

must be worth at least this much else, it will be possible to make riskless profits.

X (1+r) -T –S. < P

Consider an Example. Suppose exercise price for three- month Nifty put option is 1260.

The spot index stands at 1165 and the risk-free rate of interest is 12% per annum. In this

case the lower bound for the option price is Rs.59.80. Suppose the put is available at a

premium of Rs.45 which is less than the theoretical minimum of Rs.59.80. An arbitrageur

can borrow Rs.1210 for three months to buy both the put and the index. At the end of the

three months, the arbitrageur will be required to pay Rs.1246.3. Three months later the

option expires. At this point, the following could happen:

1. The index is below 1260, in which case the arbitrageur exercises his option, sells the

index at Rs.1260, repays the loan amount of Rs.1246.3 and makes a profit of Rs.13.7.


2. The index is above 1260 at say 1275, in which case the arbitrageur discards the option,

sells the index at 1275, repays the loan amount of Rs.1246.3 and makes an even greater

profit of 1275 - 1246.3 = Rs.28.7.


Bibliography

Books

1. Options Futures, and other Derivatives by John C Hull

2. Derivatives FAQ by Ajay Shah

3. NSE’s Certification in Financial Markets: - Derivatives Core module

4. Investment Monitor Magazine July 2001

Reports

1. Regulatory framework for financial derivatives in India by Dr. L.C.Gupta

2. Risk containment in the derivatives markets by Prof.J.R.Verma

Websites


www.derivativesindia.com

www.nse-india.com

www.sebi.gov.in

www.rediff/money/derivatives.htm

www.igidr.ac.in/~ajayshah

www.iinvestor.com

www.appliederivatives.com

www.erivativesreview.com

www.economictimes.com

www.cboe.com (Chicago Board of Exchange)

www.adtading.com

www.numa.org


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Derivatives Project Report

Documents

Transcript of Derivatives Project Report