Option General

8/8/2019 Option General

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Option PricingOption PricingTheory &Theory &

Financial OptionsFinancial Options

4848



What is an option?What is an option?

An option provides the holder with the An option provides the holder with therightright to buy or sellto buy or sell a specified quantity of a specified quantity of

an underlying asset at a fixed price (calledan underlying asset at a fixed price (called

aa strike pricestrike price or anor an exercise priceexercise price)) onon or or before the expiration datebefore the expiration date of the option.of the option.

Since it is a right andSince it is a right and not an obligationnot an obligation, ,

the holder can choose not to exercise thethe holder can choose not to exercise the

right and allow the option to expire.right and allow the option to expire.

There are two types of optionsThere are two types of options -- callcall

options (options (right to buyright to buy) and) and putput options (options (rightright

to sell).to sell). 4949



Call & PutCall & Put

Buyer of a call optionBuyer of a call option ± ± long calllong call

Seller of a call optionSeller of a call option ± ± short callshort call

Buyer of a put optionBuyer of a put option ± ± long putlong put

Seller of a put optionSeller of a put option ± ± Short PutShort Put

Underlying asset could beUnderlying asset could be

Stocks, bonds, commodity, indices, foreignStocks, bonds, commodity, indices, foreign

currency &currency & real assets.real assets.

5050



Call OptionsCall Options

A call option gives the buyer of the option A call option gives the buyer of the optionthethe right to buy the underlying assetright to buy the underlying asset at aat a

fixed price (fixed price (strike price or , X or Kstrike price or , X or K) at any) at any

time on/ before the expiration date of thetime on/ before the expiration date of theoption.option.

The buyer pays aThe buyer pays a price for this rightprice for this right ± ± CallCall

premiumpremium

5151



Call OptionCall Option

At expiration, At expiration, If the value of the underlying asset (S) > StrikeIf the value of the underlying asset (S) > Strike

Price(K)Price(K) Buyer exercises the optionBuyer exercises the option..

Call option buyer benefit:Call option buyer benefit: S S -- KK

If the value of the underlying asset (S) < Strike PriceIf the value of the underlying asset (S) < Strike Price(K)(K)

Buyer does not exerciseBuyer does not exercise

Payoff on exercise date isPayoff on exercise date is Max [ (SMax [ (STT--K), 0]K), 0] More generally,More generally,

thethe value of a call increases as the value of thevalue of a call increases as the value of theunderlying asset increasesunderlying asset increases

the value of a call decreases as the value of thethe value of a call decreases as the value of theunderlying asset decreasesunderlying asset decreases

5252



Option TypesOption Types

American American && EuropeanEuropean Types.Types.

5353



Long CallLong Call on Powergridon Powergrid

Profit fromProfit from buyingbuying one PowerGridone PowerGrid EuropeanEuropean call option:call option:Call premium = Rs.5, strike price = Rs.100, option life =Call premium = Rs.5, strike price = Rs.100, option life =2 months2 months

30

20

10

0-5

70 80 90 100

110 120 130

Profit (Rs.)

Terminalstock price (Rs.)

5454



Short CallShort Call on PowerGridon PowerGrid

Profit fromProfit from writing/sellingwriting/selling oneone PowerGridPowerGrid EuropeanEuropean callcall

option: Option Premium = Rs.5, strike price = Rs.100option: Option Premium = Rs.5, strike price = Rs.100

-30

-20

-10

05

70 80 90 100

110 120 130

Profit (Rs.)

Terminal

stock price (Rs.)

5555



ZERO SUM GAME???ZERO SUM GAME???

5656



Put OptionsPut Options

A put option gives the buyer of the option A put option gives the buyer of the optionthe right tothe right to sell the underlying assetsell the underlying asset at aat a

fixed price on/at any time before the expiryfixed price on/at any time before the expiry

date of the option.date of the option.

The buyer pays aThe buyer pays a price for this rightprice for this right ± ± putput

premiumpremium

5757



Put OptionsPut Options At expiration, At expiration,

If the value of the underlying asset (S) < Strike Price(K)If the value of the underlying asset (S) < Strike Price(K)

Put option buyer profit :Put option buyer profit : KK--SS

If the value of the underlying asset (S) > Strike Price (K)If the value of the underlying asset (S) > Strike Price (K)

Buyer does not exerciseBuyer does not exercise

Payoff on exercise date isPayoff on exercise date is Max [ (KMax [ (K-- SSTT), 0]), 0]

More generally,More generally, thethe value of a put decreasesvalue of a put decreases as theas the value of the underlying assetvalue of the underlying asset

increasesincreases thethe value of a put increasesvalue of a put increases as theas the value of the underlying assetvalue of the underlying asset

decreasesdecreases

5858



Long Put on KSOIL Long Put on KSOIL

Profit fromProfit from buyingbuying an KSOIL an KSOIL European putEuropean put option: Putoption: Put

premium = Rs.7, strike price = Rs.70premium = Rs.7, strike price = Rs.70

5959



Long Put on KSOILLong Put on KSOIL

Profit from buying an KSOIL European put option: PutProfit from buying an KSOIL European put option: Put

premium = Rs.7, strike price = Rs.70premium = Rs.7, strike price = Rs.70

30

20

10

0

-770605040 80 90 100

Profit (Rs.)

Terminal

stock price (Rs)

6060



Short Put on KSOILShort Put on KSOIL

Profit fromProfit from writingwriting an KSOIL an KSOIL European putEuropean put option: optionoption: option

price = Rs.7, strike price = Rs.70price = Rs.7, strike price = Rs.70

-30

-20

-10

7

070

605040

80 90 100

Profit (Rs.)Terminal

stock price (Rs.)

6161



Position Profit/Loss

Long Call/Call Holder

Long Put/Put Holder

Unlimited profit

potential & limited loss

to the tune of premium

Short Call/Call Writer

Short Put/Put Writer

Limited profit to the

tune of premium &

unlimited loss

6262



Options TypeOptions Type

An option is An option is inin--thethe--money (ITM)money (ITM) optionoption when itwhen it

isis pr of itablepr of itable for the option holder , if exercised.for the option holder , if exercised.

And option is And option is outout--of of--moneymoney (OTM)(OTM) when thewhen the

option holder looses money if exercises theoption holder looses money if exercises the

option.option.

An option is An option is atat--thethe--moneymoney (ATM)(ATM) when thewhen theunderlying stock price is identical or relativelyunderlying stock price is identical or relatively

close to the option strike price.close to the option strike price.

6363



Understanding Call & Put OptionUnderstanding Call & Put Option

Quotation from Financial DailiesQuotation from Financial Dailies Nifty options contracts haveNifty options contracts have 3 consecutive3 consecutive

monthly contractsmonthly contracts, additionally, additionally 3 quarterly3 quarterly

monthsmonths of the cycleof the cycle March / June / September /March / June / September /

December December andand 55 followingfollowing semisemi--annual monthsannual monthsof the cycleof the cycle June / December June / December would bewould be

available, so that at any point in time there wouldavailable, so that at any point in time there would

be options contracts with atleastbe options contracts with atleast 3 year tenure3 year tenure

availableavailable

Option QuotationOption Quotation

NIFTY Option detailsNIFTY Option details

6464



NIFTYNIFTY--50 Quotations ( 1550 Quotations ( 15thth Sep 2010)Sep 2010)

24 no. Sep 1024 no. Sep 10 callcall options with strike price (4000options with strike price (4000± ±6400)6400)

1717 nono.. OctOct1010 callcall optionsoptions withwith strikestrike priceprice ((48004800--64006400))..

1212 nono.. NovNov1010 callcall optionsoptions withwith strikestrike priceprice ((53005300--63006300))..

24 no. Sep1024 no. Sep10 putput options with strike price (4000options with strike price (4000--5300)5300)

14 No. Oct1014 No. Oct10 putput optionsoptions with strike price (4800with strike price (4800--5900).5900).

Variation in Option PremiumVariation in Option Premium::

For SepFor Sep 10 call option only10 call option only, premium varies from, premium varies fromRs.1.85 to Rs. 1819.40Rs.1.85 to Rs. 1819.40

For Sep 10 Put option, premium varies from Rs. 0.85For Sep 10 Put option, premium varies from Rs. 0.85to Rs.480.85to Rs.480.85

WHY????WHY????

6565



Option PremiumOption Premium

Two componentsTwo components

Intrinsic ValueIntrinsic Value

Time ValueTime Value Intrinsic Value: Benefit the option buyer Intrinsic Value: Benefit the option buyer

will get, if the option is exercised now.will get, if the option is exercised now.

Call Option : SCall Option : S00 ± ± EE

Put Option: EPut Option: E ± ± SS00..

6666



ITM, OTM & ATMITM, OTM & ATM

Premiums: ITM > ATM > OTMPremiums: ITM > ATM > OTM

WHY OTM contracts have value???WHY OTM contracts have value???

Premiums =Premiums =Intrinsic valueIntrinsic value ++ time valuetime value CECE--40004000--SepSep call premiumcall premium of Rs.1818.40of Rs.1818.40

Spot Nifty isSpot Nifty is 5795.255795.25

Intrinsic ValueIntrinsic Value = 5795.25= 5795.25 ± ± 4000 =1795.254000 =1795.25

Time ValueTime Value = Call premium= Call premium ± ± Intrinsic value =Intrinsic value =23.1523.15

6767




CECE--40004000--SepSep call premiumcall premium of Rs.1818.40of Rs.1818.40 Spot Nifty isSpot Nifty is 5795.255795.25

Intrinsic ValueIntrinsic Value = 1795.25= 1795.25 Time ValueTime Value = 23.15= 23.15

CECE--53005300--Sep call premium of Rs.528.65Sep call premium of Rs.528.65 Spot Nifty:Spot Nifty: 5795.255795.25

Intrinsic valueIntrinsic value = 495.25= 495.25 Time ValueTime Value = ??= ??

PEPE--40004000--Sep with a put premium of Rs.1.30, Sep with a put premium of Rs.1.30, Spot Nifty:Spot Nifty: 5795.255795.25

Intrinsic valueIntrinsic value = ??= ?? Time ValueTime Value = ??= ??

PEPE--59005900--Sep with a put premium of Rs.120.65Sep with a put premium of Rs.120.65

Spot Nifty:Spot Nifty: 5795.255795.25

Intrinsic valueIntrinsic value = 104.75= 104.75 Time ValueTime Value = ??= ??

6868




CECE--41004100--Sep isSep is DeepDeep--inin--thethe--moneymoney callcall

CECE--64006400--Sep isSep is DeepDeep--outout--of of--moneymoney callcall PEPE--42004200--Sep isSep is DeepDeep--outout--of of--moneymoney putput

PEPE--63006300--Sep isSep is DeepDeep--inin--thethe--moneymoney putput

6969



Option Premium & Time ValueOption Premium & Time Value

OptionOption PremiumPremium

CECE--60006000--SepSep 15.9015.90

CECE--60006000--OctOct 32.6532.65

CECE--60006000--NocNoc 90.0090.00

CECE--60006000-- DecDec 136.15136.15

Time premium increases as Time-to-Maturity increases

7070



Open InterestOpen Interest

Measures the liquidity in the given optionMeasures the liquidity in the given option

series.series.

7171



7272



Option Trading & SettlementOption Trading & Settlement

TheThe electr onicelectr onic order order matchingmatching systemsystem of of NSENSEisis knownknown asas NEATNEAT (National(National ExchangeExchange for for

Automated Automated Trading)Trading) whilewhile thatthat of of BSEBSE isis knownknown

asas DTSSDTSS (Derivative(Derivative TradingTrading andand SettlementSettlementSystem)System)..

OptionsOptions cancan bebe squaredsquared off off anytimeanytime beforebefore thethematuritymaturity..

Exer cisingExer cising anan optionoption andand squaringsquaring of of anan openopenpositionposition areare diff erentdiff erent..

SquaringSquaring off off meansmeans thatthat thethe trader trader entersenters intointo ananexactexact oppositeopposite contractcontract for for thethe samesame underlying,underlying,samesame maturitymaturity andand samesame strikestrike priceprice..

7373



Option Trading & SettlementOption Trading & Settlement

Squaring Off Squaring Off

A A longlong callcall positionposition entersenters intointo aa shortshort callcall positionposition..

InitiallyInitially hehe gavegave thethe callcall premiumpremium andand whilewhile squaringsquaring off off

willwill receivereceive thethe callcall premiumpremium.. SimilarlySimilarly aa trader trader withwith aashortshort callcall willwill enter enter intointo aa contractcontract for for longlong callcall..

Only ITM options are exer cisedOnly ITM options are exer cised.. So when aSo when a

trader is exercising his option, he receives the differentialtrader is exercising his option, he receives the differentialamount between the option strike price and the marketamount between the option strike price and the market

price/settlement price of the underlying asset.price/settlement price of the underlying asset.

7474



PUTPUT--C ALL RATIOC ALL RATIO

Put/call ratio = put option OI /call option OIPut/call ratio = put option OI /call option OI

It is used to measure the level of publicIt is used to measure the level of publicbullishness or bearishness in the market atbullishness or bearishness in the market at

a given time.a given time.

7575





Factors affecting option premiumFactors affecting option premium

Variables Relating to Underlying AssetVariables Relating to Underlying Asset

Expected dividends on the assetExpected dividends on the asset, which are, which are

likely to reduce the price appreciationlikely to reduce the price appreciation

component of the asset, reducing the value of component of the asset, reducing the value of

calls and increasing the value of puts.calls and increasing the value of puts.

7777



Factors affecting option premiumFactors affecting option premium

Variables Relating to OptionVariables Relating to Option

Strike Price of OptionsStrike Price of Options; the right to buy (sell); the right to buy (sell)

at a fixed price becomes more (less) valuableat a fixed price becomes more (less) valuable

at aat a lower lower strike price.strike price.

Life of the OptionLife of the Option; both calls and puts benefit; both calls and puts benefit

from a longer life.from a longer life.

Level of Interest RatesLevel of Interest Rates; As rate increases, ; As rate increases, the right tothe right to buybuy ((sellsell) at a fixed price in the) at a fixed price in the

future becomesfuture becomes moremore ((lessless) valuable.) valuable.

7878



Determinants of Option ValueDeterminants of Option Value

Factor Factor CallCallpremiumpremium

PutPutpremiumpremium

Increase in stock priceIncrease in stock price

Increase in strike priceIncrease in strike priceIncrease in variance of Increase in variance of

underlying assetunderlying asset

Increase in time to expirationIncrease in time to expiration

Increase in interest rateIncrease in interest rate

Increase in dividend paidIncrease in dividend paid

7979



Determinants of Option ValueDeterminants of Option Value

Factor Factor CallCallValueValue

PutPutValueValue

Increase in stock priceIncrease in stock price

Increase in strike priceIncrease in strike price Increase in variance of Increase in variance of

underlying assetunderlying asset

Increase in time to expirationIncrease in time to expiration Increase in interest rateIncrease in interest rate

Increase in dividend paidIncrease in dividend paid 8080



Put Call ParityPut Call Parity

C + PV (K) = S + PC + PV (K) = S + P

Holds true for European Option.Holds true for European Option.

If this equation does not hold good thenIf this equation does not hold good thenarbitrage will happenarbitrage will happen..

If the underlying asset is expectedIf the underlying asset is expected

generate Dividend ( D)generate Dividend ( D) C + D+ PV (K) = S + PC + D+ PV (K) = S + P

8181



Put Call ParityPut Call Parity

For For American Option American Option Put Call Parity does notPut Call Parity does not

hold good in absolute sense.hold good in absolute sense.

With dividend, With dividend,

( )S K C P S PV K e e

( )S D S e e

8282





What is Standard Deviation ?What is Standard Deviation ?

If 6If 6thth Feb price Rs. 85.05, what would be priceFeb price Rs. 85.05, what would be priceonon 77thth February 2010February 2010

Annual SD = 3.99% Annual SD = 3.99% Deviation for 1 day = 3.99% * Sqrt(1/252) =Deviation for 1 day = 3.99% * Sqrt(1/252) =

0.25%0.25%

Annual STDDEV (Daily Price): 3.99% Annual STDDEV (Daily Price): 3.99%

Standard Deviation: 1 dayStandard Deviation: 1 day 0.25%0.25% Standard Deviation 1 weekStandard Deviation 1 week 0.56%0.56%

Standard Deviation 1 Month 1.170%Standard Deviation 1 Month 1.170%

8484



Standard Deviation & PriceStandard Deviation & Price

Price onPrice on

77thth February 2010: 85.05February 2010: 85.05 1(0.25%*85.05) =1(0.25%*85.05) =85.0585.05 0.21 =0.21 = 84.84 to 85.26 ( Probability:84.84 to 85.26 ( Probability:68.27%)68.27%)

77thth February 2010: 85.05February 2010: 85.05 2(0.25%*85.05) =2(0.25%*85.05) =85.0585.05 0.43 =0.43 = 84.62 to 87.05 ( Probability:84.62 to 87.05 ( Probability:95.45%)95.45%)

77thth February 2010 : 85.05February 2010 : 85.05 3 (0.25%*85.05) =3 (0.25%*85.05) =

85.0585.05 0.64 =0.64 = 84.41 to 85.59 (Probability:84.41 to 85.59 (Probability:99.73%)99.73%)

Probability figures comes from the assumptionProbability figures comes from the assumptionthat stock returns follow normal distributionthat stock returns follow normal distribution..

8585



Standard NormalStandard Normal DistributionDistribution

8686



8787





Option Pricing ModelOption Pricing Model

Binomial OptionBinomial Option Pricing ModelPricing Model

Black Scholes OptionBlack Scholes Option Pricing ModelPricing Model

TheThe binomial modelbinomial model is ais a discretediscrete--timetimemodelmodel for asset price movements, with afor asset price movements, with a

time interval (t) between pricetime interval (t) between price

movements.The stock can jump to onlymovements.The stock can jump to only

one of two pointsone of two points in each time interval, andin each time interval, and

the option value is estimatedthe option value is estimated iterativelyiteratively..

8989



Stock Price = Rs.22

Option Price = Rs.1

Stock Price = Rs.18Option Price = Rs.00

Stock price = Rs.20

Option Price=?

Valuing a call option usingValuing a call option using

Binomial option pricing methodBinomial option pricing method A A 33--month call optionmonth call option on the stock has aon the stock has a strike pricestrike price of of

Rs.21. RiskRs.21. Risk--Free rate of interest = 12% per annum.Free rate of interest = 12% per annum.

9090



Binomial Option PricingBinomial Option Pricing RiskRisk--NeutralNeutral

ValuationValuation

SinceSince p p isis the probabilitythe probability that gives a return on thethat gives a return on the stockstockequal to the riskequal to the risk--free ratefree rate..

We can find it fromWe can find it from 2020ee0.120.12 vv0.250.25 == 2222 p p + 18(1+ 18(1 ± ± p p ))

which giveswhich gives p p = 0.6523= 0.6523

Alternatively, we can use the formula Alternatively, we can use the formula

6523.0

9.01.1

9.00.250.12

!

!

!

e

d u

d e p

rT

S 0u = 22u = 1

S 0d = 18

d = 0

S 0

9191



Valuing the Option Using RiskValuing the Option Using Risk--

Neutral ValuationNeutral Valuation

The value of the option isThe value of the option is

ee ± ±0.120.12vv0.250.25 ((0.65230.6523vv1 + 0.34771 + 0.3477vv00))

== 0.6330.633

S 0u = 22

u = 1

S 0d = 18

d = 0

S 0

9292



ChoosingChoosing uu andand d d

One way of matching the volatility is to setOne way of matching the volatility is to set

wherewhere WW is the volatility andis the volatility and ((t t is the lengthis the length

of the time step. This is the approach usedof the time step. This is the approach usedbyby Cox, Ross, and RubinsteinCox, Ross, and Rubinstein

1

t

t

u e

d u e

W

W

(

(

!

! !

9393



The Probability of an Up MoveThe Probability of an Up Move

( )

( )

for a non dividend p aying s tock

for a s tock index w here i s the dividen d

yie ld o n the ind ex

for a currency w here i s the fore ign

risk-free

f

r t

r q t

r r t

f

a d p

u d

a e

a e q

a e r

(

(

(

!

!

!

!

rate

1 for a futures con tracta !

9494



WorkWork --OutOut

A 6 A 6--month call option on the stock has amonth call option on the stock has a

strike price of 300. Riskstrike price of 300. Risk--Free rate of Free rate of

Interest = 12% per annum. Current marketInterest = 12% per annum. Current market

price is Rs. 310 and u = 1.5 and p =price is Rs. 310 and u = 1.5 and p =

0.6523.0.6523. Find out the Call premiumFind out the Call premium ??

9595



A Two A Two--Step ExampleStep Example

A 6 A 6--month call option on the stock has a strikemonth call option on the stock has a strike

price of 21.price of 21.

Each time step is 3 monthsEach time step is 3 months

X=21, r=12%X=21, r=12%

20

22

18

24.2

19.8

16.2

9696



Valuing a Call OptionValuing a Call Option

Value at nodeValue at node BB

== ee ± ±0.120.12vv0.250.25(0.6523(0.6523vv3.2 + 0.34773.2 + 0.3477vv0) =0) = 2.02572.0257

Value at nodeValue at node A A

== ee ± ±0.120.12vv0.250.25(0.6523(0.6523vv2.0257 + 0.34772.0257 + 0.3477vv0) =0) = 1.28231.2823

20

1.2823

22

18

24.2

3.2

19.8

0.0

16.2

0.0

2.0257

0.0

A

B

C

D

E

F

9797



Valuing a Put OptionValuing a Put Option

A 6 A 6--month put option on the stock has amonth put option on the stock has a

strike price of 300. Riskstrike price of 300. Risk--Free rate of Free rate of

Interest = 12% per annum. Current marketInterest = 12% per annum. Current market

price is Rs. 310 and u = 1.5 and p =price is Rs. 310 and u = 1.5 and p =

0.6523.0.6523. Find out the put premiumFind out the put premium ??

9898



Put Option ValuationPut Option Valuation

K K = 52, S= 50, time period = 2 years in time step= 52, S= 50, time period = 2 years in time step ==1yr , 1yr , r r = 5% per annum= 5% per annum

Value the Put option. p= 0.6282.Value the Put option. p= 0.6282. Find the putFind the putpremiumpremium

50

4.1923

60

40

720

48

4

32

20

1.4147

9.4636

A

B

C

D

E

F

9999



What Happens When an Option isWhat Happens When an Option is American ? American ?

At each node,

we have to check whether early At each node,

we have to check whether earlyexercise is better.exercise is better. At At node Bnode B, payoff from early exercise is negative 8, payoff from early exercise is negative 8 ± ± notnot

optimaloptimal

At At node Cnode C, payoff from early exercise is 12. At this node, , payoff from early exercise is 12. At this node,

the option value is 9.4636the option value is 9.4636 Hence at node C, the option value will be 12.Hence at node C, the option value will be 12.

505.0894

60

40

72

0

484

32

20

1.4147

12.0

A

B

C

D

E

F100100



Everything remaining as it is, an AmericanEverything remaining as it is, an American

option premium ________ Europeanoption premium ________ European

Option.Option.

101101



Option Pricing ModelOption Pricing Model

TheThe BlackBlack--Scholes modelScholes model applies whenapplies when

thethe underlying assetunderlying asset returnreturn distribution isdistribution is

the nor mal distributionthe nor mal distribution , and explicitly, and explicitly

assumes that the price process isassumes that the price process is

continuous and that there are no jumps incontinuous and that there are no jumps in

asset prices.asset prices.

102102



The BlackThe Black--Scholes ModelScholes Model

The value of a call/put option in the B&S The value of a call/put option in the B&S model can be written as a function of themodel can be written as a function of thefollowing variables:following variables:

S =S = Current value of the underlying assetCurrent value of the underlying assetK =K = Strike price of the optionStrike price of the option

t =t = Life to expiration of the optionLife to expiration of the option

r =r = Riskless interest rate corresponding to theRiskless interest rate corresponding to thelife of the optionlife of the option

WW22 == Variance in the of the underlying assetVariance in the of the underlying assetreturnreturn

103103



The BlackThe Black--Scholes FormulasScholes Formulas

0 1 2

2 0 1

0

1

0

2 1

( ) ( )

( ) ( )

2ln( / ) ( / 2)

2ln( / ) ( / 2)

rT

rT

c S N d K e N d

p K e N d S N d

S K r T d

T

S K r T d d T

T

W

W

W

W

W

!

!

!

! !

104104



The Normal DistributionThe Normal Distribution

Normal Distribution TableNormal Distribution Table

Normsdist( )Normsdist( ) function of Msfunction of Ms--Excel alsoExcel also

gives the value.gives the value.

105105



Adjusting for Dividends Adjusting for Dividends

If the dividend yield (If the dividend yield (yy = dividends/ Current= dividends/ Currentvalue of the asset) of the underlying asset isvalue of the asset) of the underlying asset is

expected to remain unchanged during the lifeexpected to remain unchanged during the life

of the option, the Model is modifiedof the option, the Model is modified C = S eC = S e--yytt N(dN(d11)) -- K eK e--rtrt N(dN(d22))

dd22 = d= d11 -- WW ¥t¥t

2

1

Sl n + ( r - y + ) t

K 2d =t

W

W

¨ ¸

© ¹ª º

106106



ExampleExample MTNL share is quotingMTNL share is quoting Rs.130Rs.130 today. The risktoday. The risk--free ratefree rate

of interest is 6 per cent, the time to maturity is 3 months, of interest is 6 per cent, the time to maturity is 3 months, the exercise price is Rs.140 and thethe exercise price is Rs.140 and the volatility is 20 per volatility is 20 per cent per annumcent per annum. No dividend is expected within 3 months.. No dividend is expected within 3 months.

SS == 130130

XX == 140140

r r == 0.06 or 6% per annum0.06 or 6% per annumWW == 0.20 or 20%0.20 or 20%

TT == 0.25 years0.25 years

d1 =d1 = --0.54110.5411 N(d1) = 0.2942N(d1) = 0.2942

d2 =d2 = --0.64110.6411 N(d2) = 0.2607N(d2) = 0.2607

Call value = 2.29Call value = 2.29

107107



Assignment Assignment

XYZ Co. share is quotingXYZ Co. share is quoting Rs.130Rs.130 today. Thetoday. Theriskrisk--free rate of interest is 6 per cent, the time tofree rate of interest is 6 per cent, the time tomaturity is 3 months, the exercise price ismaturity is 3 months, the exercise price isRs.140 and theRs.140 and the volatility is 20 per cent per volatility is 20 per cent per

annumannum. SYZ Co. is expected to pay Rs. 3.50 as. SYZ Co. is expected to pay Rs. 3.50 asdividend 45 days from today.dividend 45 days from today. Value the callValue the callOption.Option.

108108



Option Calculator Option Calculator

Option Calculator which uses BlackOption Calculator which uses Black--ScholesScholes

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.asp.asp

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IMPLIED VOL ATILITYIMPLIED VOL ATILITY

Option Premium is available. Find outOption Premium is available. Find out

UseUse to find out what is going to be theto find out what is going to be theoption premium for other series.option premium for other series.

114114

INDIA VIXINDIA VIX



INDI A VIXINDI A VIX

Volatility Index is a measure of market¶s expectation of Volatility Index is a measure of market¶s expectation of volatility over the near term. Volatility is often describedvolatility over the near term. Volatility is often describedas the ³rate and magnitude of changes in prices´ and inas the ³rate and magnitude of changes in prices´ and infinance often referred to as risk.finance often referred to as risk.

Volatility Index is a measure, of the amount by whichVolatility Index is a measure, of the amount by whichan underlying Index is expected to fluctuate, in the near an underlying Index is expected to fluctuate, in the near term, (calculated as annualised volatility, denoted interm, (calculated as annualised volatility, denoted inpercentage e.g. 20%) based on the order book of thepercentage e.g. 20%) based on the order book of theunderlying index options.underlying index options.

India VIX for 08India VIX for 08--SepSep--20082008

PrevioPrevio

usus

CloseClose

OpenOpen HighHigh HighHigh

TimeTime

LowLow LowLow

TimeTime

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ee

%%

ChangeChange

32.6532.65 38.2738.27 56.1956.19 11.2511.25 28.2628.26 15.0115.01 30.7730.77 --1.881.88 --5.76%5.76%

115115



INDI A VIXINDI A VIX

India VIX is a volatility index based on theIndia VIX is a volatility index based on the

Nifty 50 Index Option prices. From theNifty 50 Index Option prices. From the

best bidbest bid--ask prices of Nifty 50 Optionsask prices of Nifty 50 Options

contracts, a volatility figure (%) iscontracts, a volatility figure (%) iscalculated which indicates the expectedcalculated which indicates the expected

market volatility over the next 30 calendar market volatility over the next 30 calendar

days.days.

INDI A VIX METHODOLOGYINDI A VIX METHODOLOGY

116116



QuizQuiz

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ESOP & Bl kESOP & Bl k S h lS h l O tiO ti



ESOP & BlackESOP & Black ScholesScholes OptionOption

PricingPricing SUZLON Annual reportSUZLON Annual report (page 60).(page 60).

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