Derivatives for MMS_1

8/8/2019 Derivatives for MMS_1

1/40

Different Asset ClassesDifferent Asset Classes

EquityEquity

DebtDebt

Gold & other commoditiesGold & other commodities Real EstateReal Estate

Foreign Exchange & CurrencyForeign Exchange & Currency

DerivativesDerivatives


2/40

What do you mean by Risk ?What do you mean by Risk ?

How do you measure Risk?How do you measure Risk?

How do you reduce risk ?How do you reduce risk ?


3/40

DerivativesDerivatives

Derivative is a product whose value isDerivative is a product whose value is

derived from the value of the underlyingderived from the value of the underlying

asset.asset. Underlying asset can be equity, forex,Underlying asset can be equity, forex,

commodity, or any other asset.commodity, or any other asset.


4/40

History of DerivativesHistory of Derivatives

Chicago Board of Trade (1848) is the firstChicago Board of Trade (1848) is the first

recognised Futures Exchangerecognised Futures Exchange

Next 100 years Futures Exchanges wereNext 100 years Futures Exchanges weredominated by trading in futures ofdominated by trading in futures of

Agricultural commoditiesAgricultural commodities

1970 saw the introduction of futures on1970 saw the introduction of futures onFinancial instruments (equity, bonds &Financial instruments (equity, bonds &

currency)currency)


5/40

Features:Features: Defined & limited lifeDefined & limited life

Bilateral AgreementBilateral Agreement

Purpose:Purpose: Price DiscoveryPrice Discovery

Risk Management /Risk Management /

HedgingHedging

Making Markets moreMaking Markets more

efficientefficient

Lowering TransactionLowering Transaction

costscosts

Derivatives are often criticised as being Dangerous for

unknowledgeable investors & have been inappropriately linked

to Gambling


6/40

Classification of DerivativesClassification of Derivatives

Derivatives

Contingent Claims Forward Commitment

Exchange Traded OTCExchange Traded OTC

Standard Options

Int Rate Options

Warrants

Options on Futures

Callable Bonds

Convertible Bonds

Standard Options

Int Rate Options

Convertible Bonds

Exotic Options

Warrants

Asset Backed Sec

Forward Contract

Swaps


7/40

Forward ContractForward Contract

A Forward Contract is an agreementA Forward Contract is an agreementbetween two parties in which one party,between two parties in which one party,the buyer, agrees to buy from the otherthe buyer, agrees to buy from the other

party, the seller, an underlying asset orparty, the seller, an underlying asset orother derivative, at a future date at a priceother derivative, at a future date at a priceestablished at the start of the Contract.established at the start of the Contract.

The buyer is often called the long & theThe buyer is often called the long & theseller is often called the short.seller is often called the short.


8/40

FeaturesFeatures

Delivery & Settlement of a ForwardDelivery & Settlement of a Forward

ContractContract

Default RiskDefault Risk

Termination of a Forward ContractTermination of a Forward Contract


9/40

Types of Forward ContractTypes of Forward Contract Equity ForwardsEquity Forwards::

Forward Contracts on Individual StockForward Contracts on Individual Stock

Forward Contracts on Stock PortfoliosForward Contracts on Stock Portfolios

Forward Contracts on Stock IndicesForward Contracts on Stock Indices

Bond & Interest Rate Forward ContractsBond & Interest Rate Forward Contracts:: Forward Contracts on Individual Bonds & BondForward Contracts on Individual Bonds & Bond

PortfolioPortfolio

Forward Contracts on Interest Rates: Forwards RateForward Contracts on Interest Rates: Forwards Rate

AgreementsAgreements

Currency Forward ContractsCurrency Forward Contracts

Commodity ForwardsCommodity Forwards


10/40

Pricing a Forward ContractPricing a Forward Contract

We use the principle of NoWe use the principle of No--arbitrage for pricing aarbitrage for pricing aForward contract. The principle assumes theForward contract. The principle assumes thefollowingfollowing

Transaction cost is ZeroTransaction cost is Zero

There are no restrictions on short sales or onThere are no restrictions on short sales or onuse of short sales proceedsuse of short sales proceeds

Borrowing & Lending for unlimited amount at riskBorrowing & Lending for unlimited amount at riskfree ratefree rate

Forward price = price that would not permitForward price = price that would not permitrisk less arbitrage in frictionless marketrisk less arbitrage in frictionless market


11/40

FP = SFP = S00 x (1+Rx (1+Rff))TT

FP = Forward price of an assetFP = Forward price of an asset

SS00 = Spot price= Spot price

RRff= Risk free rate= Risk free rate

T = Forward Contract term in yearsT = Forward Contract term in years

SS00 = FP / (1+R= FP / (1+Rff))TT

Price of a Forward ContractPrice of a Forward Contract


12/40

Valuation of a Forward ContractValuation of a Forward Contract

Value of the Long Forward Contract at Zero dayValue of the Long Forward Contract at Zero day

VV00 = S= S00 FP / (1+RFP / (1+Rff))TT

Value of the Long Forward Contract at any day tValue of the Long Forward Contract at any day t

VVtt = S= Stt FP / (1+RFP / (1+Rff))(T(T--t)t)

Value of the Long Forward Contract at ExpiryValue of the Long Forward Contract at Expiry

VVtt = S= Stt FPFP


13/40

Valuation of a Forward ContractValuation of a Forward Contract

Value of the short Forward Contract at Zero dayValue of the short Forward Contract at Zero day

VV00 = FP / (1+R= FP / (1+Rff))TT SS00

Value of the short Forward Contract at any day tValue of the short Forward Contract at any day t

VVtt = FP / (1+R= FP / (1+Rff))(T(T--t)t) SStt

Value of the short Forward Contract at ExpiryValue of the short Forward Contract at Expiry

VVtt = FP= FP SStt


14/40

Equity Forward ContractEquity Forward Contract

FPFP(on an equity security)(on an equity security)= (S= (S00 PVD) x (1+RPVD) x (1+Rff))TT

FPFP(on an equity security)(on an equity security)= [S= [S00 x (1+Rx (1+Rff))TT]] -- FVDFVD

PVD = Present Value of Expected DividendsPVD = Present Value of Expected Dividends

FVD = Future Value of Expected DividendsFVD = Future Value of Expected Dividends


15/40

Value of Equity Forward ContractValue of Equity Forward Contract

For a long contractFor a long contract

VVtt = [S= [Stt PVDPVDtt]] [FP / (1+R[FP / (1+Rff))(T(T--t)t) ]]

For a short contractFor a short contract

VVtt= [FP / (1+R= [FP / (1+R

ff)) (T(T--t)t) ]] [S[S

tt PVDPVD

tt]]


16/40

Pricing a Equity Index ForwardPricing a Equity Index Forward

ContractContract Equity index has multiple stocksEquity index has multiple stocks

Rather than taking the present value ofRather than taking the present value of

dividends each individual stock, we makedividends each individual stock, we makethe calculations, as if dividends are paidthe calculations, as if dividends are paid

continuously at dividend yield on the Indexcontinuously at dividend yield on the Index

FPFP(on an equity index)(on an equity index)= S= S00 xx ee(R(Rcc cc) x T) x T

= (S= (S00 xx ee ccx Tx T ) x e) x eRR

ccxTxT

RRcc = continuous compounded risk free rate= continuous compounded risk free rate

cc = continuous compounded dividend yield= continuous compounded dividend yield


17/40

Forward contracts on Fixed IncomeForward contracts on Fixed Income

Securities & RatesSecurities & Rates Forward price on a coupon paying bond isForward price on a coupon paying bond is

similar to dividend paying stocksimilar to dividend paying stock

FPFP(fixed income security)(fixed income security)= (S= (S00 PVC) x (1+RPVC) x (1+Rff))TT

For a long contractFor a long contract

VVtt = [S= [Stt PVCPVCtt]] [FP / (1+R[FP / (1+Rff))(T(T--t)t) ]]

PVC = Present Value of Expected Coupon paymentsPVC = Present Value of Expected Coupon payments


18/40

Forward Rate Agreements (FRA)Forward Rate Agreements (FRA)

Today 3m

1m 4mToday

FRA

initiation

FRA

Expiration

& Loan

Initiation

Loan

Maturity

FRAFRA 1x41x4

Forward price in a FRA is actually a forwardForward price in a FRA is actually a forwardinterest rateinterest rate


19/40

Currency ForwardsCurrency Forwards

Consider a importer who has to make a USDConsider a importer who has to make a USDpayment 12 months from nowpayment 12 months from now

Thus, he would have to buy USD exactly 12Thus, he would have to buy USD exactly 12months from nowmonths from now

However, he is not sure what the USD/INRHowever, he is not sure what the USD/INR

rate would be???rate would be???

Hence, he can enter into aHence, he can enter into a Forward contractForward contractto buy USD 12 months from now at a preto buy USD 12 months from now at a pre--

determined ratedetermined rate


20/40

Calculated as follows: Combination of spotCalculated as follows: Combination of spot

exchange rate and interest rates over a period ofexchange rate and interest rates over a period of

time in the futuretime in the future

Forward rate: 45,687,500 / 1,020,000 = 44.79Forward rate: 45,687,500 / 1,020,000 = 44.79

Forward premium: 2.29Forward premium: 2.29

Bank buys USD at 42.50

Gets USD 1,020,000

Places Deposit @ 2.00%

Borrows INR 42,500,000

Pays INR 45,687,500

Borrows at 7.50%

USD / INR: 42.50, US Int rates: 2.00%, Indian Interest rates: 7.50%


21/40

Futures and stockFutures and stock

FPFP(currency forward contract )(currency forward contract ) ==

SS00 x [(1+Rx [(1+RDCDC))TT/(1+R/(1+RFCFC))

TT]]

F and S are quoted in domestic currency perF and S are quoted in domestic currency per

unit of foreign currencyunit of foreign currency

RRDCDC = Domestic currency interest rate= Domestic currency interest rate

RRFCFC = Foreign currency interest rate= Foreign currency interest rate


22/40

FuturesFutures

Similarity to Forwards:Similarity to Forwards:

Deliverable contracts obligate the long toDeliverable contracts obligate the long tobuy & short to sell a certain quantity of anbuy & short to sell a certain quantity of anasset for a certain price on specified futureasset for a certain price on specified futuredatedate

Cash settlements are settled in cash onCash settlements are settled in cash on

expiration dateexpiration date Both futures & forwards are priced to haveBoth futures & forwards are priced to have

zero value at the time of initiationzero value at the time of initiation


23/40

Futures Vs ForwardsFutures Vs Forwards

CriterionCriterion FuturesFutures ForwardsForwards

BuyerBuyer--SellerSeller

InteractionInteraction

Via ExchangeVia Exchange DirectDirect

Contract TermsContract Terms StandardisedStandardised Tailor madeTailor made

UnilateralUnilateral

ReversalsReversals

PossiblePossible Not PossibleNot Possible

Default risk borneDefault risk borne

byby

ExchangeExchange Individual PartiesIndividual Parties

Default ControlledDefault Controlled

byby

Margin AccountsMargin Accounts CollateralsCollaterals


24/40

Payoff profile of futures contractsPayoff profile of futures contracts

-100

-50

0

50

100

5000 5050 5100 5150 5200

Price

Gain/Loss

Buyer

Seller

Profit

Loss


25/40

Future Margins & MTMFuture Margins & MTM

Initial Margin RequirementInitial Margin Requirement

Maintenance MarginMaintenance Margin

Variation MarginVariation Margin


26/40

Calculation of Margin for a Long positionCalculation of Margin for a Long position

Day Beginning

Balance

(Margin)

Funds

Deposited

Settlement

Price

Futures

Price

Change

Gain /

Loss

Ending

Balance

(Margin)

0 0 50 100.00 50.00

1 50 0 99.20 -0.80 -8.00 42.00

2 42 0 96.00 -3.20 -32.00 10.00

3 10 40 101.00 5.00 50.00 100.00

4 100 0 103.50 2.50 25.00 125.00

5 125 0 103.00 -0.50 -5.00 120.00

6 120 0 104.00 1.00 10.00 130.00

Initial Futures prices: Rs.100; Initial Margin: Rs.5;Maintenance Margin Requirement: Rs.3; No of Contracts:10


27/40

Monetary & Non Monetary benefitsMonetary & Non Monetary benefits

& costs of holding the Underlying& costs of holding the Underlying

Recall:Recall: FP = SFP = S00 x (1+Rx (1+Rff))TT

Any positive costs associated with holdingAny positive costs associated with holding

the asset in a cash & carry arbitrage willthe asset in a cash & carry arbitrage willincrease the no arbitrage Futures priceincrease the no arbitrage Futures price

A monetary benefit from holding the assetA monetary benefit from holding the assetwill decrease the no arbitrage Futureswill decrease the no arbitrage Futurespriceprice


28/40


29/40

BackwardationBackwardation: refers to a situation: refers to a situation

where the futures price is below the spotwhere the futures price is below the spot

price.price.

For this to occur, there must be significantFor this to occur, there must be significant

benefit to holding the asset, eitherbenefit to holding the asset, either

monetary or nonmonetary or non--monetary.monetary.

ContangoContango: refers to a situation where the: refers to a situation where the

futures price is above the spot pricefutures price is above the spot price


30/40

Consider an asset priced at Rs.50. Risk freeConsider an asset priced at Rs.50. Risk freeinterest rate is 8% & the futures contract expiresinterest rate is 8% & the futures contract expiresin 45 days.in 45 days.

a.a. Find the appropriate futures price if theFind the appropriate futures price if theunderlying asset has no storage cost, cash flowsunderlying asset has no storage cost, cash flowsor convenience yieldor convenience yield

b.b. Find the appropriate futures prices if the futureFind the appropriate futures prices if the futurevalue of storage cost on the underlying at thevalue of storage cost on the underlying at the

futures expiration equals Rs.2.25futures expiration equals Rs.2.25c.c. Find the appropriate futures price if the futureFind the appropriate futures price if the future

value of positive cash flow on the underlyingvalue of positive cash flow on the underlyingasset equals Rs.0.75asset equals Rs.0.75

d.d. Find the appropriate futures price if the futureFind the appropriate futures price if the futurevalue of the net overall cost of carry on thevalue of the net overall cost of carry on theunderlying asset equals Rs.3.55underlying asset equals Rs.3.55

e.e. Using Part D above, illustrate how an arbitrageUsing Part D above, illustrate how an arbitragetransaction could be executed if the futurestransaction could be executed if the futures

contract is trading at Rs.60contract is trading at Rs.60


31/40

OptionsOptions

CallCall OptionsOptions

AA callcall optionoption givesgives thethe holderholder (buyer/(buyer/ oneone whowho isislonglong call),call), thethe rightright toto buybuy specifiedspecified quantityquantity ofof

thethe underlyingunderlying assetasset atat thethe strikestrike priceprice onon or orbeforebefore expirationexpiration datedate..

TheThe sellerseller (one(one whowho isis shortshort call)call) however,however, hashas

thethe obligationobligation toto sellsell thethe underlyingunderlying assetasset ifif thethebuyerbuyer ofof thethe callcall optionoption decidesdecides toto exerciseexercise hishisoptionoption toto buybuy..


32/40

AnAn investorinvestor buysbuys OneOne EuropeanEuropean callcall optionoption ononInfosysInfosys atat thethe strikestrike priceprice ofof RsRs.. 25002500 atat aa premiumpremiumofof RsRs.. 100100.. IfIf thethe marketmarket priceprice ofof InfosysInfosys onon thethe dayday

ofof expiryexpiry isis moremore thanthan RsRs.. 25002500,, thethe optionoption willwill bebeexercisedexercised..

TheThe investorinvestor willwill earnearn profitsprofits onceonce thethe shareshare priceprice

crossescrosses RsRs.. 26002600 (Strike(Strike PricePrice ++ PremiumPremium ii..ee..25002500++100100))..

SupposeSuppose stockstock priceprice isis RsRs.. 28002800,, thethe optionoption willwill bebe

exercisedexercised andand thethe investorinvestor willwill buybuy 11 shareshare of ofInfosysInfosys fromfrom thethe sellerseller ofof thethe optionoption atat RsRs 25002500 andandsellsell itit inin thethe marketmarket atat RsRs 28002800 makingmaking aa profitprofit ofof RsRs..200200 {(Spot{(Spot priceprice -- StrikeStrike price)price) -- Premium}Premium}


33/40

PutPut OptionsOptions

AA PutPut optionoption givesgives thethe holderholder (buyer/(buyer/ oneone whowho isislonglong Put),Put), thethe rightright toto sellsell specifiedspecified quantityquantity ofof

thethe underlyingunderlying assetasset atat thethe strikestrike priceprice onon or orbeforebefore anan expiryexpiry datedate..

TheThe sellerseller ofof thethe putput optionoption (one(one whowho isis shortshort

Put)Put) however,however, hashas thethe obligationobligation toto buybuy thetheunderlyingunderlying assetasset atat thethe strikestrike priceprice ifif thethe buyerbuyerdecidesdecides toto exerciseexercise hishis optionoption toto sellsell..


34/40

An investor buys one European Put option onAn investor buys one European Put option onReliance at the strike price of Rs. 2300/Reliance at the strike price of Rs. 2300/-- , at a, at apremium of Rs. 125/premium of Rs. 125/--. If the market price of. If the market price of

Reliance, on the day of expiry is less than Rs. 300,Reliance, on the day of expiry is less than Rs. 300,the option can be exercised as it is 'in the money'.the option can be exercised as it is 'in the money'.

The investor's BreakThe investor's Break--even point is Rs. 2175/ (Strikeeven point is Rs. 2175/ (StrikePricePrice -- premium paid) i.e., investor will earn profits ifpremium paid) i.e., investor will earn profits if

the market falls below 2175.the market falls below 2175.

Suppose stock price is Rs. 2160, the buyer of theSuppose stock price is Rs. 2160, the buyer of thePut option immediately buys Reliance share in thePut option immediately buys Reliance share in themarket @ Rs. 2160/market @ Rs. 2160/-- & exercises his option selling& exercises his option selling

the Reliance share at Rs 2300 to the option writerthe Reliance share at Rs 2300 to the option writerthus making a net profit of Rs. 15 {(Strike pricethus making a net profit of Rs. 15 {(Strike price --Spot Price)Spot Price) -- Premium paid}Premium paid}


35/40

Position of Call option buyerPosition of Call option buyer

Traders rightsTraders rights-- Buy underlying at strike price.Buy underlying at strike price.

Traders obligationsTraders obligations-- Nil.Nil.

Premium paid or receivedPremium paid or received -- Paid.Paid.

Margin requirementsMargin requirements -- No.No.

Risk profileRisk profile -- Limited, to the extent of theLimited, to the extent of the

premium paid.premium paid.

Profit potentialProfit potential -- Unlimited, if prices go up.Unlimited, if prices go up. Breakeven pointBreakeven point -- Strike price + Premium.Strike price + Premium.


36/40

Position of Call option sellerPosition of Call option seller

Traders rightsTraders rights-- Nil.Nil.

Traders obligationsTraders obligations-- Sell underlying at strikeSell underlying at strike

price.price.

Premium paid or receivedPremium paid or received -- Received.Received.

Margin requirementsMargin requirements -- Yes.Yes.

Risk profileRisk profile -- Unlimited, if prices go up.Unlimited, if prices go up.

Profit potentialProfit potential -- Limited , to the extent of theLimited , to the extent of thepremium received.premium received.

Breakeven pointBreakeven point -- Strike price + Premium.Strike price + Premium.


37/40

Payoff profile of Call optionsPayoff profile of Call options

tri e Pre i

-20

-15

-10

-5

0

5

10

15

20

90 95 100 105 110 115 120

Price

Profit/Loss

Buyer

Writer


38/40

Position of Put option buyerPosition of Put option buyer

Traders rightsTraders rights-- Sell underlying at strike price.Sell underlying at strike price.

Traders obligationsTraders obligations-- Nil.Nil.

Premium paid or receivedPremium paid or received -- Paid.Paid.

Margin requirementsMargin requirements -- No.No.

Risk profileRisk profile -- Limited, to the extent of theLimited, to the extent of thepremium paid.premium paid.

Profit potentialProfit potential -- Unlimited*, if prices go downUnlimited*, if prices go down(BEP = Strike price(BEP = Strike price -- Premium).Premium).

Practically, Put option buyers profit is limited asPractically, Put option buyers profit is limited asthe price of the asset can not go below zerothe price of the asset can not go below zero(Max. profit = Strike price(Max. profit = Strike price Premium paid)Premium paid)


39/40

Position of Put option sellerPosition of Put option seller

Traders rightsTraders rights-- Nil.Nil.

Traders obligationsTraders obligations-- Buy underlying at strike price.Buy underlying at strike price.

Premium paid or receivedPremium paid or received -- Received.Received.

Margin requirementsMargin requirements -- Yes.Yes. Risk profileRisk profile -- Unlimited*, if prices go down.Unlimited*, if prices go down.

Profit potentialProfit potential -- Limited, to the extent of theLimited, to the extent of thepremium received (BEP = Strike pricepremium received (BEP = Strike price -- Premium)Premium)

Practically, Put option sellers risk is limited as thePractically, Put option sellers risk is limited as theprice of the asset can not go below zeroprice of the asset can not go below zero(Maximum loss = Strike price(Maximum loss = Strike price Premium received)Premium received)


40/40

Payoff profile of Put optionsPayoff profile of Put options

Strike : 100 & Premium :5

-15

-10

-5

0

5

10

15

85 90 95 100 105 110 115

Price

P

rofit/Loss

Buyer

Writer

Derivatives for MMS_1

Documents

Transcript of Derivatives for MMS_1