option general
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Option PricingOption PricingTheory &Theory &
Financial OptionsFinancial Options
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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
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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 ¤cy & real assets.real assets.
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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
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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
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Option TypesOption Types
American American && EuropeanEuropean Types.Types.
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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.)
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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.)
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ZERO SUM GAME???ZERO SUM GAME???
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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
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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
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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
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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)
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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.)
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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
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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.
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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
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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????
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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..
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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
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ITM, OTM & ATMITM, OTM & ATM
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 = ??= ??
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ITM, OTM & ATMITM, OTM & ATM
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
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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
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Open InterestOpen Interest
Measures the liquidity in the given optionMeasures the liquidity in the given option
series.series.
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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..
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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.
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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.
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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.
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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.
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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
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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
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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
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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
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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%
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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..
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Standard NormalStandard Normal DistributionDistribution
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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..
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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.
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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
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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
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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
(
(
!
! !
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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 !
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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 ??
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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
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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
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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 ??
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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
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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
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Everything remaining as it is, an AmericanEverything remaining as it is, an American
option premium ________ Europeanoption premium ________ European
Option.Option.
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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.
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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
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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
!
!
!
! !
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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.
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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
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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
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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.
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Option Calculator Option Calculator
Option Calculator which uses BlackOption Calculator which uses Black--ScholesScholes
Option Pricing formula.Option Pricing formula.
http://www.bseindia.com/derivatives/optioncalchttp://www.bseindia.com/derivatives/optioncalc
.asp.asp
Forms a base price.Forms a base price.
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110110
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Trinomial Tree (Hull 6th edition)
S S
S d
S u
pu
pm
pd
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Trinomial Tree (Hull 6th edition)
6
1
212
3
2
6
1
212
/1
2
2
2
2
3
¹¹ º
¸©©ª
¨ W
W
(!
!
¹¹ º
¸
©©ª
¨ W
W
(
!
!!(W
r t
p
p
r t
p
ud eu
d
m
u
t
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Trinomial Tree (Boyle 1986)
d u
t r
d
t r
u
t t
p p p
d u
eu p
d u
d e p
ed eu
!
¹
¹¹
º
¸
©
©©
ª
¨
!
¹¹¹
º
¸
©©©
ª
¨
!
!!!
(
(
((
1
1/u
2
2
2
2
22 W W
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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.
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INDIA VIXINDIA VIX
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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
CloseClose ChangChang
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%
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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
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QuizQuiz
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ESOP & Bl kESOP & Bl k S h lS h l O tiO ti
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ESOP & BlackESOP & Black ScholesScholes OptionOption
PricingPricing SUZLON Annual reportSUZLON Annual report (page 60).(page 60).