Derivatives Market 51542

7/31/2019 Derivatives Market 51542

1/45

Winter Project M.B.A Sem IV

BLACK SCHOLES MODEL AND DERIVATIVESMARKET IN INDIA

DEPARTMENT OF MANAGEMENT STUDIESKUMAUN UNIVERSITY NAINITAL

SUBMITTED TO:SUBMITTED BY:

Dr. L.K.SINGHBRIJESH SHAH

Head of Department ROLLNO. 51542DMS BHIMTAL Enroll No.

KU985410


2/45

STUDENTS DECLARATION

This project has been undertaken as a partial fulfillment ofthe requirements for the award of the Degree of Master inbusiness Administration of Kumaun University, Nainital.

I hereby declare that this project is my original work &analysis & findings are for academic purpose only. Thesuggestions given are solely the result of my interpretationand not to harm organizational interests. This project has notbeen presented in any seminar or submitted elsewhere for

the award of any degree or any diploma.

Counter signed by: Sign. Of Student

Dr. L.K.Singh (HOD) BRIJESHSHAH Dept. of Management StudiesIVth, SemesterCampus Bhimtal, NainitalRoll No. 51542

ACKNOWLEDGEMENT


3/45

I herewith take the opportunity to express my profound

sense of gratitude and reverence to all those who have

helped and encouraged me towards the successful

completion of the project.

I would like to pay special regards to Dr.L.K.Singh (Project

guide) for guiding me and for showing keen interest that

helped me in materializing the work.

CONTENT SHEET

Chapter (I)

1.1 Introduction


4/45

Financial Derivative markets

Need of Derivative Market

The participants in Derivatives market

Types of Derivatives

1.2 Introduction to Futures

1.3 Commodity Derivatives

Chapter (II)

2.1 Research Methodology

Chapter (III)

3.1Development of Derivatives Market in India

Chapter (IV)

4.1 Analysis & Interpretation

Chapter (V)

5.1 Conclusions & Suggestions

Bibliography

Annexure


5/45

CHAPTER (I)

INTRODUCTION OF DERIVATIVES

MARKETS

Financial Derivatives Market:

Financial markets are, by nature, extremely volatile andhence the risk factor is an important concern for financialagents. To reduce this risk, the concept of derivatives comes


6/45

into the picture. Derivatives are products whose values arederived from one or more basic variables called bases. Thesebases can be underlying assets (for example forex, equity,etc), bases or reference rates. For example, wheat farmers

may wish to sell their harvest at a future date to eliminatethe risk of a change in prices by that date. The transaction inthis case would be the derivative, while the spot price ofwheat would be the underlying asset.

Development of exchange-tradedderivatives

Derivatives have probably been around for as long as peoplehave been trading with one another. Forward contractingdates back at least to the 12th century and may well havebeen around before then. Merchants entered into contractswith one another for future delivery of specified amount ofcommodities at specified price. A primary motivation for pre-arranging a buyer or seller for a stock of commodities inearly forward contracts was to lessen the possibility thatlarge swings would inhibit marketing the commodity after aharvest.

The need for a derivatives market

The derivatives market performs a number of economicfunctions:

1. They help in transferring risks from risk adverse peopleto risk oriented people


7/45

2. They help in the discovery of future as well as currentprices.

3. They catalyze entrepreneurial activity.

4. They increase the volume traded in markets because ofparticipation of risk adverse people in greater numbers.

5. They increase savings and investment in the long run.

The participants in a derivatives market

Hedgers:

Hedgers are those who protect themselves from the riskassociated with the price of an asset by using derivatives. A

person keeps a close watch upon the prices discovered in tradingand when the comfortable price is reflected according to hiswants, he sells futures contracts. In this way he gets an assuredfixed price of his produce.

In general, hedgers use futures for protection against adversefuture price movements in the underlying cash commodity.


8/45

Hedgers are often businesses, or individuals, who at one point oranother deal in the underlying cash commodity.

Take an example: A Hedger pays more to the farmer or dealer of

a produce if its prices go up. For protection against higher pricesof the produce, he hedges the risk exposure by buying enoughfuture contracts of the produce to cover the amount of producehe expects to buy. Since cash and futures prices do tend to movein tandem, the futures position will profit if the price of theproduce raise enough to offset cash loss on the produce.

Arbitragers:

According to dictionary definition, a person who has beenofficially chosen to make a decision between two people orgroups who do not agree is known as Arbitragers. In commoditymarket Arbitragers are the person who takes the advantage of adiscrepancy between prices in two different markets. If he findsfuture prices of a commodity edging out with the cash price, hewill take offsetting positions in both the markets to lock in aprofit. Moreover the commodity futures investor is not chargedinterest on the difference between margin and the full contract

value.

Speculators:

Speculators are somewhat like a middleman. They are neverinterested in actual owing the commodity. They will just buyfrom one end and sell it to the other in anticipation of futureprice movements. They actually bet on the future movementin the price of an asset.

They are the second major group of futures players. Theseparticipants include independent floor traders and investors.They handle trades for their personal clients or brokeragefirms.


9/45

Buying a futures contract in anticipation of price increases isknown as going long. Selling a futures contract inanticipation of a price decrease is known as going short.Speculative participation in futures trading has increased

with the availability of alternative methods ofparticipation.

Speculators have certain advantages over other investmentsthey are as follows:

If the traders judgment is good, he can make moremoney in the futures market faster because pricestend, on average, to change more quickly than realestate or stock prices.

Futures are highly leveraged investments. The traderputs up a small fraction of the value of the underlyingcontract as margin, yet he can ride on the full value ofthe contract as it moves up and down. The money heputs up is not a down payment on the underlyingcontract, but a performance bond. The actual value ofthe contract is only exchanged on those rare occasionswhen delivery takes place.

Types of Derivatives

Forwards: A forward contract is a customized contractbetween two entities, where settlement takes place on aspecific date in the future at todays pre-agreed price.

Futures: A futures contract is an agreement between twoparties to buy or sell an asset at a certain time in the futureat a certain price. Futures contracts are special types offorward contracts in the sense that the former arestandardized exchange-traded contracts


10/45

Options: Options are of two types - calls and puts. Callsgive the buyer the right but not the obligation to buy a givenquantity of the underlying asset, at a given price on orbefore a given future date. Puts give the buyer the right, but

not the obligation to sell a given quantity of the underlyingasset at a given price on or before a given date.

Warrants: Options generally have lives of up to one year,the majority of options traded on options exchanges havinga maximum maturity of nine months. Longer-dated optionsare called warrants and are generally traded over-the-counter.

LEAPS:The acronym LEAPS means Long-Term EquityAnticipation Securities. These are options having a maturityof up to three years.

Baskets: Basket options are options on portfolios ofunderlying assets. The underlying asset is usually a movingaverage or a basket of assets. Equity index options are aform of basket options.

Swaps: Swaps are private agreements between two partiesto exchange cash flows in the future according to aprearranged formula. They can be regarded as portfolios offorward contracts. The two commonly used swaps are:

Interest rate swaps: These entail swapping only theinterest related cash flows between the parties in the samecurrency.

Currency swaps: These entail swapping both principaland interest between the parties, with the cash flows in one


11/45

direction being in a different currency than those in theopposite direction.

Swaptions: Swaptions are options to buy or sell a swap thatwill become operative at the expiry of the options. Thus aswaption is an option on a forward swap. Rather than havecalls and puts, the swaptions market has receiver swaptionsand payer swaptions. A receiver swaption is an option toreceive fixed and pay floating. A payer swaption is an optionto pay fixed and receive floating.

FEATURES OF AN OPTION

Call option: A call option gives the buyer `the right but notthe obligation' to buy the stock at a specified price on afuture date.

Put Option: A put option gives the buyer `the right but notthe obligation' to sell a stock at a given price on a futuredate.

Exercise: Options on individual stocks are American andhence can be exercised at any date before expiration. Indexoptions are European and can be exercised only on theexpiration date


12/45

Call/Put premium: The price paid by the buyer of a calloption or a put option is termed as the call/put premium. Thepremium is a one time outflow for the buyer of options.

Expiration Date: Expiration date is the day on which theoption contract matures. The expiration date in the case ofoptions on both the NSE and BSE is fixed as the lastThursday of the respective month.

Strike: The strike price is the price at which an option canbe exercised. For instance the Nifty 26th July 1020 strike calloption means that the investor can exercise the call optionon the Nifty on 26th July at a price of 1020.

High Price The high price refers to the highest premiumcharged on an option for the entire week.

Low Price The low price refers to the lowest premiumcharged on an option for the entire week.

Average Close The average close represents theaverage premium calculated from the last traded price on alldays for the trading week.

Spot Close The spot close refers to the last traded priceof the underlying in the cash market on the last trading day.

Aggregate Traded Quantity Aggregate traded quantityrefers to the total traded quantity for an option during thecourse of the week.

Average Notional Value Average notional value refersto the average notional value of a contract traded during thecourse of the week.


13/45

Factors driving the growth of financialderivatives

1. Increased volatility in asset prices in financial markets,

2. Increased integration of national financial markets withthe international markets,

3. Marked improvement in communication facilities andsharp decline in their costs,

4. Development of more sophisticated risk managementtools, providing economic agents a wider choice of riskmanagement strategies, and

5. Innovations in the derivatives markets, which optimallycombine the risks and returns over a large number offinancial assets leading to higher returns, reduced riskas well as transactions costs as compared to individualfinancial assets.

Commodity Derivatives

Futures contracts in pepper, turmeric, gur (jaggery), hessian(jute fabric), jute sacking, castor seed, potato, coffee, cotton,and soybean and its derivatives are traded in 18 commodityexchanges located in various parts of the country. Futures

trading in other edible oils, oilseeds and oil cakes have beenpermitted. Trading in futures in the new commodities,especially in edible oils, is expected to commence in thenear future. The sugar industry is exploring the merits oftrading sugar futures contracts. The policy initiatives and themodernization programme include extensive training,structuring a reliable clearinghouse, establishment of a


14/45

system of warehouse receipts, and the thrust towards theestablishment of a national commodity exchange. TheGovernment of India has constituted a committee to exploreand evaluate issues pertinent to the establishment and

funding of the proposed national commodity exchange forthe nationwide trading of commodity futures contracts, andthe other institutions and institutional processes such aswarehousing and clearinghouses.With commodity futures, delivery is best affected usingwarehouse receipts (which are like dematerializedsecurities). Warehousing functions have enabled viableexchanges to augment their strengths in contract design andtrading. The viability of the national commodity exchange ispredicated on the reliability of the warehousing functions.

The programme for establishing a system of warehousereceipts is in progress. The Coffee Futures Exchange India(COFEI) has operated a system of warehouse receipts since1998

Exchange-traded vs. OTC (Over the Counter)derivatives markets

The OTC derivatives markets have witnessed rather sharpgrowth over the last few years, which have accompanied themodernization of commercial and investment banking andglobalization of financial activities. The recent developmentsin information technology have contributed to a great extentto these developments. While both exchange-traded andOTC derivative contracts offer many benefits, the former

have rigid structures compared to the latter. It has beenwidely discussed that the highly leveraged institutions andtheir OTC derivative positions were the main cause ofturbulence in financial markets in 1998. These episodes ofturbulence revealed the risks posed to market stabilityoriginating in features of OTC derivative instruments andmarkets.


15/45

The OTC derivatives markets have the following featurescompared to exchange-traded derivatives:

1. The management of counter-party (credit) risk isdecentralized and located within individual institutions.

2. There are no formal centralized limits on individualpositions, leverage, or margining.

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

4. There are no formal rules or mechanisms for ensuringmarket stability and integrity, and for safeguarding the

collective interests of market participants.

5. The OTC contracts are generally not regulated by aregulatory authority and the exchanges self-regulatoryorganization, although they are affected indirectly bynational legal systems, banking supervision and marketsurveillance.

Accounting of Derivatives:

The Institute of Chartered Accountants of India (ICAI) hasissued guidance notes on accounting of index futurescontracts from the viewpoint of parties who enter into suchfutures contracts as buyers or sellers. For other partiesinvolved in the trading process, like brokers, tradingmembers, clearing members and clearing corporations, atrade in equity index futures is similar to a trade in, sayshares, and does not pose any peculiar accounting problems.

Taxation

The income tax Act does not have any specific provisionregarding taxability from derivatives. The only provisions,which have an indirect bearing on derivative transactions,


16/45

are sections 73(1) and 43(5). Section 73(1) provides that anyloss, computed in respect of a speculative business carriedon by the assessee, shall not be set off except against profitsand gains, if any, of speculative business. In the absence of

a specific provision, it is apprehended that the derivativescontracts, particularly the index futures which are essentiallycash-settled, may be construed as speculative transactionsand therefore the losses, if any, will not be eligible for set offagainst other income of the assessee and will be carriedforward and set off against speculative income only up to amaximum of eight years .As a result an investors losses orprofits out of derivatives even though they are of hedgingnature in real sense, are treated as speculative and can beset off only against speculative income.

CHAPTER (II)


17/45

RESEARCH METHODOLOGY

Research Methodology

Introduction to problem:

Derivatives entered Indian Capital market in Jun.2000.Derivatives are still in developing stage because of the riskand uncertainty behind it. So, I am trying to analyse the riskinvolved in Derivatives market by applying Black-Scholesmodel on four established Companies stock price.

Research Objective:

1. To analyse the growth of derivatives market.2. To study Black-Scholes model.

3. To understand the volatility of stock in the selected fourcompanies.


18/45

Research Design:

If we are conversant with the problem of theenvironment conducting the investigation for some

definite purpose with the help of a structural formulato gather information as much as possible. This typeof research design is descriptive research design.Appropriate tools and techniques are used for theanalysis. Generally the derivative tool is used foranalyzing the project. The data put in the models foranalysis and the resulting scores reportedappropriately. For analyzing the data I use BlackScholes Model.

Collection of Data:

Data are collected through websites and completely based

on sampling. The source of data is based on national stockexchange of India website and THE ECONOMICS TIMES.

Secondary data:

It can define as data collected by someone else forpurpose other than solving the problem being investigation.Data are collected through census method based on the

Stock prices of companies for the month of April.

Analysis and Reporting:

Appropriate tools and techniques are used for the analysis.Generally the statically tools are used for analyzing the


19/45

project. The data put in the models for analysis and theresulting scores reported appropriately. For analyzing thedata I use Black-Scholes Model.

Limitation of the study:

Time and availability of the data are some of the factor thatconfined the scope of our study.

CHAPTER (III)

DEVELOPMENT OF DERIVATIVESMARKETS IN INDIA


20/45

Development of derivatives market in India

The first step towards introduction of derivatives trading inIndia was the promulgation of the Securities Laws(Amendment) Ordinance, 1995, which withdrew theprohibition on options in securities. The market forderivatives, however, did not take off, as there was noregulatory framework to govern trading of derivatives. SEBIset up a 24member committee under the Chairmanship ofDr.L.C.Gupta on November 18, 1996 to develop appropriate

regulatory framework for derivatives trading in India. Thecommittee submitted its report on March 17, 1998prescribing necessary preconditions for introduction ofderivatives trading in India. The committee recommendedthat derivatives should be declared as securities so thatregulatory framework applicable to trading of securitiescould also govern trading of securities. SEBI also set up agroup in June 1998 under the Chairmanship ofProf.J.R.Varma, to recommend measures for risk

containment in derivatives market in India. The report, whichwas submitted in October 1998, worked out the operationaldetails of margining system, methodology for charging initialmargins, broker net worth, deposit requirement and realtime monitoring requirements. The Securities ContractRegulation Act (SCRA) was amended in December 1999 toinclude derivatives within the ambit of securities and the


21/45

regulatory framework were developed for governingderivatives trading. The act also made it clear thatderivatives shall be legal and valid only if such contracts aretraded on a recognized stock exchange, thus precluding OTC

derivatives. The government also rescinded in March 2000,the three decade old notification, which prohibited forwardtrading in securities.

Derivatives trading commenced in India in June 2000 afterSEBI granted the final approval to this effect in May 2001.SEBI permitted the derivative segments of two stock

exchanges, NSE and BSE, and their clearinghouse/corporation to commence trading and settlement inapproved derivatives contracts. To begin with, SEBIapproved trading in index futures contracts based on S&PCNX Nifty and BSE30(Sensex) index. This was followed byapproval for trading in options based on these two indexesand options on individual securities. The trading in BSESensex options commenced on June 4, 2001 and the tradingin options on individual securities commenced in July 2001.

Futures contracts on individual stocks were launched inNovember 2001. The derivatives trading on NSE commencedwith S&P CNX Nifty Index futures on June 12, 2000. Thetrading in index options commenced on June 4, 2001 andtrading in options on individual securities commenced onJuly 2, 2001. Single stock futures were launched onNovember 9, 2001. The index futures and options contracton NSE are based on S&P CNX Trading and settlement inderivative contracts is done in accordance with the rules,byelaws, and regulations of the respective exchanges andtheir clearing house/corporation duly approved by SEBI andnotified in the official gazette. Foreign Institutional Investors(FIIs) are permitted to trade in all Exchange tradedderivative products.


22/45

Business Growth of Derivatives Segment

Years

IndexFutures

StockFutures Futures

Index

Options

Stock

Options Options Tota

Turnover (Rs.

cr.)

Turnover (Rs.

cr.)

Turnover

(Rs.cr.)

Turnover (Rs.

cr.)

Turnover (Rs.

cr.)

Turnover (Rs.

cr.)

Turnoer (Rs

cr.)

2000-01 2,365 - 2,365 - - 0 2,32001-02 21,483 51,515 72,998 3,765 25,163 28,928 101,92002-03 43,952 286,533 330,485 9,246 100,131 109,377 439,8

2003-04 554,4461,305,9

391,860,3

85 52,816 217,207 270,0232,130

2004-05 772,1471,484,0

562,256,2

03 121,943 168,836 290,7792,546

2005-061,513,7

552,791,6

974,305,4

52 338,469 180,253 518,7224,824

2006-072,539,5

743,830,9

676,370,5

41 791,906 193,795 985,7017,356

Note:

Notional Turnover = (Strike Price + Premium) * Quantity

Index Futures, Index Options, Stock Options and StockFutures were introduced in June 2000, June 2001, July 2001and November 2001 respectively.


23/45

I n d e x F u

0

5 0 0 , 0 0 0

1 , 0 0 0 , 0 0 0

1 , 5 0 0 , 0 0 0

2 , 0 0 0 , 0 0 0

2 , 5 0 0 , 0 0 0

3 , 0 0 0 , 0 0 0

2 0 0 0 -

0 1

2 0 0 1 -

0 2

2 0 0 2 -

0 3

2 0 0 3 -

0 4

2 0 0 4 -

0 5

2 0 0 5 -

0 6

2 0 0 6 -

0 7

Y e a

Turnover(Rs.

Cr.)

S e r ie


24/45

Index Futures was introduced in June 2000. In 2000-01 theturnover of index futures was Rs.2, 365 Crores. Later thegrowth rate of index futures was 67.00% in between 2005-

06 to 2006-07. The turnover of index futures was Rs.2,539,574 Crore in 2006-07. The market Share of index futuresis 35.00% in 2006-07.


25/45

S t o c k F u

0

5 0 0 0 0 0

1 0 0 0 0 0 0

1 5 0 0 0 0 0

2 0 0 0 0 0 0

2 5 0 0 0 0 0

3 0 0 0 0 0 0

3 5 0 0 0 0 0

4 0 0 0 0 0 0

4 5 0 0 0 0 0

2 0 0 0 -

0 1

2 0 0 1 -

0 2

2 0 0 2 -

0 3

2 0 0 3 -

0 4

2 0 0 4 -

0 5

2 0 0 5 -

0 6

2 0 0 6 -

0 7

y e a

Turnover(

Rs.

Cr.)

S e r i e

Stock Futures was introduced in June 2001. In 2000-01 theturnover of stock futures was Rs. 51, 515 Crore. The growthrate of stock futures was 37.22% in between 2005-06 to

2006-07. The market share of stock futures was 51.00% in2006-07.


26/45

In d e x O p

0

1 0 0 0 0 0

2 0 0 0 0 03 0 0 0 0 0

4 0 0 0 0 0

5 0 0 0 0 0

6 0 0 0 0 0

7 0 0 0 0 0

8 0 0 0 0 0

9 0 0 0 0 0

2 0 0 0 -

0 1

2 0 0 1 -

0 2

2 0 0 2 -

0 3

2 0 0 3 -

0 4

2 0 0 4 -

0 5

2 0 0 5 -

0 6

2 0 0 6 -

0 7

Y e a

Turnover(Rs.

Cr.)

S e r i e

Index Options was introduced in July 2001. The turnover ofindex options was Rs. 3, 765 crore in 2001-02. The growthrate of index options was 133.96% in between 2005-06 to

2006-07. The market share of index options was 11% in2006-07. The turnover of index options was Rs. 791, 906Crore.


27/45

S t o c k O p

0

5 0 0 0 0

1 0 0 0 0 0

1 5 0 0 0 0

2 0 0 0 0 0

2 5 0 0 0 0

2 0 0 0 -

0 1

2 0 0 1 -

0 2

2 0 0 2 -

0 3

2 0 0 3 -

0 4

2 0 0 4 -

0 5

2 0 0 5 -

0 6

2 0 0 6 -

0 7

Y e a

Turnover

(Rs.

Cr.)

S e r ie

Stock Options was introduced in Nov. 2001. The turnover ofstock options was Rs. 25, 163 Crore. The growth rate ofstock options was 471.20% in between 2002-03 to 2003-04.After 2003-04, the turnover of stock options had been

declined. The growth rate of stock options was 7.50% inbetween 2005-06 to 2006-07. The market share of stockoptions was 3.00% in 2006-07.


28/45

T o t a l T u r

0

1 , 0 0 0 , 0 0 0

2 , 0 0 0 , 0 0 03 , 0 0 0 , 0 0 0

4 , 0 0 0 , 0 0 0

5 , 0 0 0 , 0 0 0

6 , 0 0 0 , 0 0 0

7 , 0 0 0 , 0 0 0

8 , 0 0 0 , 0 0 0

2 0 0 0 -

0 1

2 0 0 1 -

0 2

2 0 0 2 -

0 3

2 0 0 3 -

0 4

2 0 0 4 -

0 5

2 0 0 5 -

0 6

2 0 0 6 -

0 7

Y e a

urnover

s.

r.

S e r ie

The total turnover of Derivatives segment was Rs. 2,365Crore in 2000-01. The growth rate of Derivatives segment

was 52.40 % in between 2005-06 to 2006-07. The totalturnover of Derivatives segment was Rs. 7, 356, 242 Crore in2006-07.

Market Composition of Derivatives segment


29/45

2005-06

31%

58%

7%4%

Index Futures

Stock Futures

Index Options

Stock Options

2006-07

35%

51%

11%3%

Index Futures

Stock Futures

Index Options

Stock Options

From the above charts we can see that the growths in Indexmarkets (Futures and Options) are well as compared to Stockmarkets (Futures and Options).The market share of Index Options was 11 % in 2006-07 ascompared to 7% in 2005-06 which shows the growth in IndexOptions market.The market share of Index Futures was 35 % in 2006-07 ascompared to 31% in 2005-06 which shows the growth inIndex Options market.


30/45

CHAPTER (IV)

DATA ANALYSIS & INTERPRETATION


31/45

The Black Scholes Model

The model is based on a normal distribution of underlying

asset returns, which is the same thing as saying that theunderlying asset prices themselves are log normallydistributed. A lognormal distribution has a longer right tailcompared with a normal, or bell-shaped, distribution. Thelognormal distribution allows for a stock price distribution ofbetween zero and infinity (i.e. no negative prices) and has anupward bias (representing the fact that a stock price canonly drop 100% but can rise by more than 100%).

In practice underlying asset price distributions often departsignificantly from the lognormal. For example historicaldistributions of underlying asset returns often have fatter leftand right tails than a normal distribution indicating thatdramatic market moves occur with greater frequency thanwould be predicted by a normal distribution of returns-- i.e.more very high returns and more very low returns.

A corollary of this is the volatility smile -- the way in whichat-the-money options often have a lower volatility than

deeply out-of- the-money options or deeply in-the- moneyoptions.

The Black-Scholes model is used to calculate a theoreticalcall price (ignoring dividends paid during the life of theoption) using the five key determinants of an option's price:stock price, strike price, volatility, time to expiration, andshort-term (risk free) interest rate.


32/45

The original formula for calculating the theoretical optionprice (OP) is as follows:

P = S N (d1) E e-rt N (d2)

Where:

d1 = ln (S/E)+ (r + 0.5 2) t t

d2 = ln ( S /E ) + ( r - 0.5 2) t t

Also,

d2 = d1 - t

The variables are:

P=Premium of the option.

S = Current price of the stock.

E = Exercise price of the option.

t = Time remaining until expiration, expressed as a percentof a year.r = Current continuously compounded risk-free interest rate.

v = Annual volatility of stock price (the standard deviation of

the short-term returns over one year).

ln = natural logarithm.

N (d1, d2) = Standard normal cumulative distributionfunction.


33/45

e = Exponential function.

Annualized volatility () =Daily volatility 250

(250 days = 365 (52*2)-3 national holidays -8 otherholidays)

Risk free rate (r) =7.2% (source www.nseindia.com )

Computation of Volatility:

Step 1: Calculate price relative for each day and find naturallogarithms of each of the price relative.

Step 2: Calculate standard deviation of the series ofcontinuously compounded rate ofreturn

Steps 3: Convert the continuously compounded dailystandard deviation to the yearly deviation by

multiplying it by the square root of 250 days.

Step 4: The model is derived under the assumption thoserates of return are identically distributed over time.The volatility measure on the basis of historical data.

Computation of S.D

It is widely used measure of studying variation. The greaterthe amount of the variation, the greater the standard
http://www.nseindia.com/http://www.nseindia.com/


34/45

deviation, for the greater will be the magnitude of thedeviation of the values from their mean.

S.D=X2

- Mean2

N

Where,

X = Total of the values of a set of observations.

N = Total number of observations.

Mean=X2 = 0.119 =0.006 N 19

S.D=X2 - Mean2= 0.01352 (0.006) 2= .026

N 19

Standard Deviation = 0.026

Annualized Volatility ( ) = 0.026* 250 = 0.411 or 41.10 %.

S=111

E=105

R=7.2%


35/45

t=27/365=0.0739

d1 = ln (S/E) + (r + 0.5 2) tt

d1 = .0556 + (.072 +0.5*(0.411)2)*0.0739 = 0.54090.026* 0.0739

d2 = d1 - t

d2 = 0.5409 - 0.411 * 0.0739 = 0.4295

P = S N (d1) E e-rt N (d2)

=111 N (0.5409) - 105 e-rt N (0.4295)

P = 8.37

SAIL.

COMPUTATION OF CALL PREMIUM

ExpiryApril07

3-Apr-07 4-Apr-07 5-Apr-07

Current Market Price Rs.

111

Current Market Price Rs.

112

Current Market Price Rs

115

Exercise

price

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDiffere

ce

105 12.9 8.37 4.53 9.8 9.06 0.74 12.0 11.33 0.67

110 9 5.71 3.29 5.9 5.80 0.10 7.35 7.01 0.34

115 5.85 3.30 2.55 3.5 3.40 0.10 4.2 4.09 0.11


36/45

The Standard Deviations of The Steel Authority of IndiaLtd. stock is 0.026, so they are risky and the annualizedvolatility of the Steel Authority of India Ltd. stock is

41.10%, so the option premium of Steel Authority of IndiaLtd. are more valuable over and in near future stock pricemove downward or upward.

An increase in the exercise price From Rs105 to Rs115reduces the value of call option premium.

The Premium of call option decreases as the expirationdate is approaching.

Reliance Industries Ltd.


ExpiryApril 07

3-Apr-07 4-Apr-07 5-Apr-07

Current Market Price Rs.1341



Exercise price

PActual

PCalculated

Difference

PActual

PCalculated

Difference

PActual

PCalculated

Differece

1320 45.9 45.02 0.88 60.35 59.06 1.29 57.3 55.09 2.21

1350 29.9 28.07 1.83 40.4 40.08 0.32 39.35 36.60 2.75

1380 17.7 17.50 0.20 23.75 22.75 1.00 23.8 23.48 0.32


37/45

Standard Deviation =0.014 Annualized Volatility =23.24%.

The Standard Deviations of The Reliance Industries Ltd.

stock is 0.014, so they are less risky and the annualizedvolatility of the Reliance Industries Ltd. stock is 23.24%,so the call option premium of Reliance Industries lessvaluable and the stock price of Reliance are stable.


An increase in the exercise price reduces the intrinsicvalue of the call option,thus the call premium reduces

with this.

When the exercise price is greater than the stock price,than call option become out of the money.hence its valuereduces.At this point the entire premium is on account ofthe time value.

When the current market price increases, the call optionpremium increases.

ITC Ltd.


ExpiryApril

07

3-Apr-07 4-Apr-07 5-Apr-07



Current Market Price Rs148

Exercise

price

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDiffere

ce

140 11.7 10.58 1.12 11.25 9.761.4

9 9.72 9.70 0.02

145 8.4 7.13 1.27 7.256.

36 0.89 7.15 6.33 0.82


38/45

150 5.25 4.47 0.78 4.75 3.94 0.81 4.353.8

2 0.53

Standard Deviation =0.019 Annualized Volatility =

30.6%.

The Standard Deviations of The ITC Ltd. stock is 0.019 sothey are less risky and the annualized volatility of the ITCLtd. stock is 30.6%, so the call option premium of ITC ltdis valuable and the stock price of ITC will move up infuture.


When the current market prices decreases the optionpremium also decreases.

TCS Ltd.


ExpiryApril07

3-Apr-07 4-Apr-07 5-Apr-07



Current Market Price R1194

Exercise

price

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDifferen

ce

PActua

l

PCalculate

dDiffe

ce

1200 45.5 38.45 7.05 42.8 34.90 7.9 40.15 32.44


39/45

1230 32.85 25.89 6.96 29.7 22.56 7.14 28.4 21.08

1260 20.3 15.97 4.33 20.25 14.18 6.07 18.5 12.39

Standard Deviation =0.017 Annualized Volatility =28.37%.

The Standard Deviations of The Tata Consultancy ServicesLtd. stock is 0.017, so they are less risky and theannualized volatility of the Tata Consultancy Services Ltd.stock is 28.37%, so the call option premium of TataConsultancy Services Ltd. are less valuable and the stockprice of TCS will be stable in future.



40/45

CHAPTER

(V)

CONCLUSIONS & SUGGESTIONS

CONCLUSIONS

1. The Premium of a call option decreases as the expirationdate is approaching.

2. The call with the higher exercise price cannot to be valuedhigher.


41/45

3. A call option cannot have a smaller value than its intrinsicvalue.

4. Time value of option is Maximum when the price of the

stock is at exercise price.

5. A call option is more valuable when stock prices increasesand less valuable when it decreases.

6. The owner of the call benefits from the price increasesand his downward risk is limited since he can looseoption premium.

8. Longer the duration of maturity, greater is the time value

of the option premium.

9. Volatility of the stock is between 20% to 50%.

SUGGESTIONS

1. Black Scholes Model gives almost the appropriate value ofoption premium but we cannot calculate the accurate valueof option premium

2. Volatility of Stock Price gives a general idea of Stock Pricemovement.


42/45

3. Black and Scholes option pricing model works well foroptions that are near the money and for options with next

striking price on either side of the stock price.

4. Model does not yield unbiased value in respect of stockswith very high or very low volatility.

Bibliography

Books:

1. Vohra, N.D, Bagri, B.R, Futures and Options, Tata McGraw-Hill Publishing

Company Limited, New Delhi.

2. John C. Hull, Options, Futures and Other Derivatives,

Magazine:

1. Business Today


43/45

Newspaper:

1. The Economic Times

2. Business Line

Web Site:

1. www.google.com

2. www.nseindia.com

3. www.bseindia.com

4. www.derivativesindia.com

Annexure

1. Current Market Prices of four Companies in the month of April are as follows:

Date RIL SAIL ITC TCS2-Apr-07 1313.95 107.65 146.8 1189.23-Apr-07 1340.75 111.15 149.5 1202.74-Apr-07 1363.25 112.15 148.35 1198.45-Apr-07 1358.15 114.9 148.2 1194.2

9-Apr-07 1384.3 118.05 155.3 1217.210-Apr-07 1384.4 117.8 159.85 1197.411-Apr-07 1386.6 122.75 160.5 1190.612-Apr-07 1387.5 120.65 156.25 120113-Apr-07 1411.95 125.9 153.45 126216-Apr-07 1457.75 128 158.5 1280.317-Apr-07 1475.8 123.8 156.05 1250.3


44/45

18-Apr-07 1485.35 125.6 156.9 1247.519-Apr-07 1492.35 125.8 159.1 1242.920-Apr-07 1541.45 134.2 160.4 1257.723-Apr-07 1554.3 136.15 156.3 1247.8

24-Apr-07 1582.95 134.1 156.45 1224.925-Apr-07 1598.4 134.15 161.8 1221.426-Apr-07 1596.85 134.35 161.55 1240.427-Apr-07 1539.2 132.5 160.65 1234.530-Apr-07 1561.05 130.45 160.05 1266

2. Expiry, Exercise price and the Call premium of four companies.

RELIANCE

ExpiryApril07

3-Apr-07 4-Apr-07

5-Apr-07

Exerciseprice

P Actual P Actual P Actual

1200 67 60.35 57.31230 45 40.4 39.351260 29 23.75 23.8

ITCExpiry

April07

3-Apr-

07

4-Apr-

07

5-Apr-07

Exerciseprice

PActual

PActual

P Actual

1200 67 60.35 57.31230 45 40.4 39.351260 29 23.75 23.8


45/45

SAILExpiryApril07

3-Apr-07

4-Apr-07

5-Apr-07

Exerciseprice

PActual

PActual

P Actual

1200 67 60.35 57.31230 45 40.4 39.351260 29 23.75 23.8

TCSExpiryApril07

3-Apr-07

4-Apr-07

5-Apr-07

Exerciseprice

PActual

PActual

P Actual

1200 67 60.35 57.31230 45 40.4 39.35

1260 29 23.75 23.8

Derivatives Market 51542

Documents

Transcript of Derivatives Market 51542