DerivaGem - Version 1.52For Excel 2000 and more recent versions of Excel

This is the Applications Builder Software that has been designed toaccompany John Hull's texts:

"Options, Futures and Other Derivatives" 7/Eand

"Fundamentals of Futures and Options Markets" 6/E

Both books are published by Pearson Prentice Hall. They can be ordered from outlets such asAmazon.com or directly from the publisher at http://www.prenhall.com/mischtm/support_fr.html

before using this software

This software was developed for educational purposes by A-J Financial Systems, Inc.

Note: You should familiarize yourself with the Options Calculator Software in DG152.xls

Important: Do not forget to enable Macros. If you are using Office 2007 you will have toclick on the Options button and choose "Enable this Content"

DerivaGem - Version 1.52For Excel 2000 and more recent versions of Excel

This is the Applications Builder Software that has been designed toaccompany John Hull's texts:

"Options, Futures and Other Derivatives" 7/Eand

"Fundamentals of Futures and Options Markets" 6/E

Both books are published by Pearson Prentice Hall. They can be ordered from outlets such asAmazon.com or directly from the publisher at http://www.prenhall.com/mischtm/support_fr.html

before using this software

This software was developed for educational purposes by A-J Financial Systems, Inc.

: You should familiarize yourself with the Options Calculator Software in DG152.xls

Do not forget to enable Macros. If you are using Office 2007 you will have toclick on the Options button and choose "Enable this Content"

THE DERIVAGEM APPLICATIONS BUILDER CONTAINS 21 FUNCTIONS FROM WHICH USERS CAN BUILD THEIR OWN APPLICATIONSSPREADSHEETS WITH 7 SAMPLE APPLICATIONS ARE INCLUDED

Function 1: Black_Scholes(S,K,r,q,vol,T,IsCall,IsFut,Divs,Result)Carries out Black-Scholes calculations for European options on stocks, stock indices,currencies and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsCall TRUE if call, FALSE if putIsFut TRUE if futures option, FALSE otherwiseDivs Array containing time to dividend payment and size of dividend payment in cols 1 and 2. (Leave blank if not applicable)Result 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

DividendsExample: #VALUE! 0.5 1

0.75 1

Function 2: TreeEquityOpt(S,K,r,q,vol,T,IsCall,IsFut,Divs,IsAmerican,nSteps,Result)Carries out binomial tree calculations for European or American options on stocks, stock indices, currencies, and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsCall TRUE if call, FALSE if putIsFut TRUE if futures option, FALSE otherwiseDivs Array containing time to dividend payment and size of dividend payment in cols 1 and 2. (Leave blank if not applicable)IsAmerican TRUE if American option, FALSE if European optionnSteps Number of time steps on treeResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE!

Function 3: BinaryOption(S,K,r,q,vol,T,IsCall,IsFut,Divs,IsCash,Result)Carries out calculations for binary options on stocks, stock indices,currencies and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsCall TRUE if call, FALSE if putIsFut TRUE if futures option, FALSE otherwiseDivs Array containing time to dividend payment and size of dividend payment in cols 1 and 2. (Leave blank if not applicable)IsCash TRUE if Cash or Nothing, FALSE if Asset or NothingResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE! (Delta of Cash or Nothing Call)

Function 4: BarrierOption(S,K,r,q,vol,T,IsCall,IsFut,H,IsUp,IsIn,Result)Carries out calculations for barrier options on non-dividend-paying stocks, stock indices, currencies and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsCall TRUE if call, FALSE if putIsFut TRUE if futures option, FALSE otherwiseH BarrierIsUp TRUE if Up option; FALSE if Down optionIsIn TRUE if In option; FALSE if Out optionResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE! (Price of down and out call option)

Function 5: AverageOption(S,K,r,q,vol,T,IsCall,IsFut,CurrAve,TimeSoFar,Result)Carries out calculations for Asian options on non-dividend-paying stocks, stock indices,currencies and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)

T Time to maturity (yrs)IsCall TRUE if call, FALSE if putIsFut TRUE if futures option, FALSE otherwiseCurrAve Current Average (irrelevant if a new instrument)TimeSoFar Time since beginning of averaging in years (zero for a new instrument)Result 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE!

Function 6: ChooserOption(S,K,r,q,vol,T,IsFut,TimeToChoice,Result)Carries out calculations for chooser options on non-dividend-paying stocks, stock indices,currencies and futuresArguments:S Asset PriceK Strike pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsFut TRUE if futures option, FALSE otherwiseTimeToChoice Time until choice between call and put has to be madeResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE!

Function 7: CompoundOption(S,K1,r,q,vol,T1,IsCall,IsFut,K2,T2,IsOptionOnCall,Result)Carries out calculations for compound options on non-dividend-paying stocks, stock indices,currencies and futuresArguments:S Asset PriceK1 First Strike Pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T1 Time to first exerciseIsCall True if first option a call, FALSE if first option a putIsFut TRUE if futures option, FALSE otherwiseK2 Second strike priceT2 Time to second exerciseIsOptionOnCall TRUE if second option is a call, FALSE if second option is a putResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE!

Function 8: LookbackOption(S,r,q,vol,T,IsCall,IsFut,IsFixedLookback,Smax,Smin,K,Result)Carries out calculations for lookback options on non-dividend-paying stocks, stock indices,currencies and futuresArguments:S Asset Pricer Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)vol Volatility. BUT Enter Price if Implied Volatility is to be calculated (i.e. Result=6)T Time to maturity (yrs)IsCall TRUE if lookback call, FALSE if lookback putIsFut TRUE if futures option, FALSE otherwiseIsFixedLookback TRUE for fixed lookbackSmax Maximum price to date (equals to current price if a new instrument)Smin Minimum price to date (equals current price if a new instrument)K Strike price for Fixed Lookback; Ignored otherwiseResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho; 6=Implied Vol

Example #VALUE!

Function 9: EPortfolio(t,S,IsFut,r,q,Divs,vol,Portfolio,Result)Carries out calculations for a portfolio of options on a non-dividend-paying stock, stock index, currency, or futuresArguments:t Valuation date (years from today >=0)S Asset priceIsFut TRUE if underlying is a futures price; FALSE otherwiser Domestic risk-free rateq Dividend yield for stock index options, foreign risk free rate for currency options (Enter 0 if this parameter not applicable)Divs Array containing time to dividend payment and size of dividend payment in cols 1 and 2. (Leave blank if not applicable)vol VolatilityPortfolio Array defining portfolio. See belowResult 0=Price; 1=Delta; 2=Gamma; 3=Vega; 4=Theta; 5=Rho

Portfolio definition:Type

Underlying 0 NumberBlack Scholes 1 Number K T IsCallTreeEquityOption 2 Number K T IsCall nSteps IsAmericanBinaryoption 3 Number K T IsCall IsCashBarrierOption 4 Number K T IsCall Barrier IsUp IsInAverageOption 5 Number K T IsCall CurrAve TimeSoFarChooserOption 6 Number K T TimeToChoice

CompoundOption 7 Number K1 T1 IsCall K2 T2 IsOptOnCallLookBackOption 8 Number K T IsCall IsFixedLookback Smax Smin

Sample PortfolioType Number

Underlying 0 100Black Scholes 1 50 55 0.5 1Black Scholes 1 50 48 0.75 1TreeEquityOption 2 100 50 0.5 0 25 1

Example of Function: #VALUE!

Function 10: BlackCap(Start,End,CapRate,L,Frequ,vol,IsCap,Zeros,Result)Carries out calculations for caps and floors using Black's modelArguments: Term StructureStart Time (years from today) when cap starts 0 3.000%End Time (years from today) when cap ends 0.5 3.353%CapRate Cap Rate 1 3.664%L Notional amount 1.5 3.938%Frequ Number of times a year cap is settled (= 12, 4, 2, or 1) 2 4.180%vol Flat volatility. BUT enter price if implied volatility is to be calculated (i.e. Result=4) 2.5 4.394%IsCap TRUE if cap, FALSE if Floor 3 4.583%Zeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second column 3.5 4.749%Result 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=ImpliedVol 4 4.896%

4.5 5.026%Example #VALUE! 5 5.140%

5.5 5.241%6 5.331%

Function 11: HullWhiteCap(Start,End,CapRate,L,Frequ,sigma,a,IsCap,Zeros,Result) 6.5 5.409%Carries out calculations for caps and floors using Hull-White model 7 5.479%Arguments: 7.5 5.540%Start Time (years from today) when cap starts 8 5.594%End Time (years from today) when cap ends 8.5 5.642%CapRate Cap Rate 9 5.684%L Notional amount 9.5 5.721%Frequ Number of times a year cap is settled (= 12, 4, 2, or 1) 10 5.754%sigma Short rate standard deviation. But enter price if implied sigma is to be calculated (i.e.Result=4)a Reversion rateIsCap TRUE if cap, FALSE if floorZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=ImpliedVol

Example #VALUE!

Function 12: TreeCap(Start,End,CapRate,L,Frequ,sigma,a,IsCap,Model,nsteps,Zeros,Result)Carries out calculations for caps and floors usng a trinomial treeArguments:Start Time (years from today) when cap startsEnd Time (years from today) when cap endsCapRate Cap RateL Notional AmountFrequ Number of times a year cap is settled (= 12, 4, 2, or 1)sigma Volatility parametera Reversion rateIsCap TRUE if cap, FALSE if floorModel 0=Normal, 1=LognormalnSteps Number of time stepsZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 13: BlackSwapOpt(Start,End,SwapRate,L,Frequ,vol,IsPayFix,Zeros,Result)Carries out calculations for swap options usng Black's modelArguments:Start Time (years from today) when option maturesEnd Time (years from today) when underlying swap endsSwapRate Strike Swap RateL Principal amountFrequ Frequency of payments on swap (= 12, 4, 2, or 1)vol Volatility. BUT enter price if implied volatility is to be calculated (i.e. Result=4)IsPayFix TRUE if option to pay strike swap rate, FALSE if option to receive strike swap rateZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied Volatility

Example #VALUE!

Function 14: HullWhiteSwapOpt(Start,End,SwapRate,L,Frequ,sigma,a,IsPayFix,Zeros,Result)Carries out calculations for swap options using the Hull-White modelArguments:Start Time (years from today) when option matures

End Time (years from today) when underlying swap endsSwapRate Strike Swap RateL Principal amountFrequ Frequency of payments on swap (= 12, 4, 2, or 1)sigma Short rate standard deviation. But enter price if implied sigma is to be calculated (i.e.Result=4)a Reversion rateIsPayFix TRUE if option to pay strike swap rate, FALSE if option to receive strike swap rateZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 15: TreeSwapOpt(Start,End,SwapRate,L,Frequ,sigma,a,IsPayFix,Model,nSteps,Zeros,Result)Carries out calculations for swap options using a trinomial treeArguments:Start Time (years from today) when option maturesEnd Time (years from today) when underlying swap endsSwapRate Strike Swap RateL Principal amountFrequ Frequency of payments on swap (= 12, 4, 2, or 1)sigma Volatility parametera Reversion rateIsPayFix TRUE if option to pay strike swap rate, FALSE if option to receive strike swap rateModel 0=Normal, 1=Lognormalnsteps Number of time stepsZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 16: BlackBondOpt(BondLife,Coupon,Princ,Frequ,K,T,vol,IsCall,IsQuoted,Zeros,Result)Carries out calculations for bond options usng Black's modelArguments:BondLife Life of bond in years(from today)Coupon Coupon (rate per year)Princ Bond PrincipalFrequ Frequency of payments on bond (=4, 2, or 1)K Strike PriceT Time (in years) to option maturity vol Volatility. BUT enter price if implied volatility is to be calculated (i.e. Result=4)IsCall TRUE if call, FALSE if putIsQuoted True if strike is a quoted price, false if strike is cash priceZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 17: HullWhiteBondOpt(BondLife,Coupon,Princ,Frequ,K,T,sigma,a, IsCall,IsQuoted,Zeros,Result)Carries out calculations for bond options using Hull-White modelArguments:BondLife Life of bond in years(from today)Coupon Coupon (rate per year)Princ Bond PrincipalFrequ Frequency of payments on bond (=4, 2, or 1)K Strike PriceT Time (in years) to option maturity sigma Short rate standard deviation. But enter price if implied sigma is to be calculated (i.e.Result=4)a Reversion rateIsCall TRUE if call, FALSE if putIsQuoted True if strike is a quoted price, false if strike is cash priceZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 18: TreeBondOpt(BondLife,Coupon,Princ,Frequ,K,T,sigma,a, IsCall,IsQuoted,IsAmerican,Model,nSteps,Zeros,Result)Carries out calculations for bond options usng a trinomial treeArguments:BondLife Life of bond in years(from today)Coupon Coupon (rate per year) Princ Bond PrincipalFrequ Frequency of payments on bond per year (=4, 2, or 1)K Strike PriceT Time (in years) to option maturity sigma Volatility parametera Reversion rateIsCall TRUE if call, FALSE if putIsQuoted True if strike is a quoted price, false if strike is cash priceIsAmerican TRUE if American option, FALSE if EuropeanModel 0=Normal, 1=LognormalnSteps Number of time stepsZeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second column

Result 0=Price, 1=Delta, 2=Gamma, 3=Vega, 4=Implied sigma

Example #VALUE!

Function 19: BondPrice(BondLife, Coupon, Princ, Frequ, Zeros, IsClean, Result)Values a bondArguments:BondLife Life of bond in years(from today)Coupon Coupon (rate per year)Princ Bond principalFrequ Frequency of payments on bond per year (=12, 4, 2, or 1)Zeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnIsClean If TRUE result is the clean (quoted) price; if FALSE result is dirty (cash) priceResult 0=Price, 1=Delta, 2=Gamma

Example #VALUE!

Function 20: SwapPrice(Start, End, FixedRate,L,Frequ,Zeros,Result)Values a plain vanilla interest rate swap. Note: ignores cash flows arising from reset dates prior to Start dateArguments:Start Beginning of swap (years from today)End End of swap (years from today)FixedRate Fixed rate that is exchange for floating (compounding frequency corresponds to Frequ)L Notional principalFrequ Frequency of payments on swap per year (=12, 4, 2, or 1) Zeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnResult 0=Price, 1=Delta, 2=Gamma

Example #VALUE!

Function 21: IPortfolio(t,Zeros,Nsigma,Na,LNsigma,LNa, Portfolio,Result)Carries out calculations for a portfolio of options on a non-dividend-paying stock, stock index, currency, or futuresArguments:t Valuation date (years from today >=0)Zeros Array containing zero curve: Maturities in the first column and corresponding zero rates in second columnNsigma sigma parameter to be used with normal modelNa reversion rate parameter to be used with normal modelLNsigma sigma parameter to be used with lognormal modelLNa reversion rate parameter to be used with lognormal modelPortfolio Array defining portfolio. See belowResult 0=Price; 1=Delta; 2=Gamma; 3=Vega

Portfolio definition:Type

Bond 0 Life Coupon Princ. Frequ IsCleanSwap 1 Start End FixedRate L FrequBlack Cap 2 Start End CapRate L Frequ IsCap volHW Cap 3 Start End CapRate L Frequ IsCapTree Cap 4 Start End CapRate L Frequ IsCap Model nStepsBlack Swaption 5 Start End SwapRate L Frequ IsPayFix volHW Swaption 6 Start End SwapRate L Frequ IsPayFixTree Swaption 7 Start End SwapRate L Frequ IsPayFix Model nStepsBlack Bond Opt. 8 Life Coupon Princ Frequ K T IsCall IsQuoted volHW Bond Opt. 9 Life Coupon Princ Frequ K T IsCall IsQuotedTree Bond Opt. 10 Life Coupon Princ Frequ K T IsCall IsQuoted Model nSteps IsAmerican

Sample PortfolioType

Bond 0 10.2 6% 100 2 1Black Bond Opt. 8 10.2 6% 100 2 102 0.5 1 1 15%Black Bond Opt. 8 10.2 6% 100 2 105 1 1 1 14%Tree Bond Opt. 10 10.2 6% 100 2 98 5 0 1 1 25 1

Example #VALUE!

CONVERGENCE OF BINOMIAL TREE PRICE OF EUROPEAN OPTION TO BLACK-SCHOLES PRICE Figure 19.4 in Options, Futures, and Other Derivatives, 7e (and 16.4 in Fundamentals 6e) shows a similar result for an American option

Problem 19.30 in Options, Futures and Other Derivatives, 7e (and 16.7 in Fundamentals 6e) is based on this application

Stock Price 50Strike 50.1

r 5.00%q 0%

vol 40%Remaining Life 1

IsCall 0IsFut 0

Result 0

IsAmerican 0

nSteps Tree BS2 #VALUE! #VALUE!3 #VALUE! #VALUE!4 #VALUE! #VALUE!5 #VALUE! #VALUE!6 #VALUE! #VALUE!7 #VALUE! #VALUE!8 #VALUE! #VALUE!9 #VALUE! #VALUE!

10 #VALUE! #VALUE!11 #VALUE! #VALUE!12 #VALUE! #VALUE!13 #VALUE! #VALUE!14 #VALUE! #VALUE!15 #VALUE! #VALUE!16 #VALUE! #VALUE!17 #VALUE! #VALUE!18 #VALUE! #VALUE!19 #VALUE! #VALUE!20 #VALUE! #VALUE!21 #VALUE! #VALUE!22 #VALUE! #VALUE!23 #VALUE! #VALUE!24 #VALUE! #VALUE!25 #VALUE! #VALUE!26 #VALUE! #VALUE!27 #VALUE! #VALUE!28 #VALUE! #VALUE!

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

Convergence 1

Tree

BS

nSteps

29 #VALUE! #VALUE!30 #VALUE! #VALUE!31 #VALUE! #VALUE!32 #VALUE! #VALUE!33 #VALUE! #VALUE!34 #VALUE! #VALUE!35 #VALUE! #VALUE!36 #VALUE! #VALUE!37 #VALUE! #VALUE!38 #VALUE! #VALUE!39 #VALUE! #VALUE!40 #VALUE! #VALUE!41 #VALUE! #VALUE!42 #VALUE! #VALUE!43 #VALUE! #VALUE!44 #VALUE! #VALUE!45 #VALUE! #VALUE!46 #VALUE! #VALUE!47 #VALUE! #VALUE!48 #VALUE! #VALUE!49 #VALUE! #VALUE!50 #VALUE! #VALUE!

CONVERGENCE OF BINOMIAL TREE PRICE OF EUROPEAN OPTION TO BLACK-SCHOLES PRICE Figure 19.4 in Options, Futures, and Other Derivatives, 7e (and 16.4 in Fundamentals 6e) shows a similar result for an American option

Problem 19.30 in Options, Futures and Other Derivatives, 7e (and 16.7 in Fundamentals 6e) is based on this application

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

Convergence 1

Tree

BS

nSteps

PLOTS OF GREEK LETTERS

Maturity 1 Stock Price 50Strike 50 Int. Rate 0.05Int. Rate 5% Volatility 0.3Volatility 25% IsCall 1IsCall 0 Result 1Result 2 0->Price, 1->Delta, 2->Gamma, 3->Vega, 4->Theta, 5->Rho

S Result10 #VALUE! 0.00512 #VALUE! 0.0114 #VALUE! 0.0516 #VALUE! 0.1018 #VALUE! 0.1520 #VALUE! 0.2022 #VALUE! 0.2524 #VALUE! 0.3026 #VALUE! 0.3528 #VALUE! 0.4030 #VALUE! 0.4532 #VALUE! 0.5034 #VALUE! 0.5536 #VALUE! 0.6038 #VALUE! 0.6540 #VALUE! 0.7042 #VALUE! 0.7544 #VALUE! 0.8046 #VALUE! 0.8548 #VALUE! 0.9050 #VALUE! 0.9552 #VALUE! 1.0054 #VALUE! 1.2556 #VALUE! 1.5058 #VALUE! 1.7560 #VALUE! 2.0062 #VALUE! 2.2564 #VALUE! 2.5066 #VALUE! 2.7568 #VALUE! 3.0070 #VALUE! 3.2572 #VALUE! 3.5074 #VALUE! 3.7576 #VALUE! 4.0078 #VALUE! 4.2580 #VALUE! 4.5082 #VALUE! 4.7584 #VALUE! 5.0086 #VALUE!88 #VALUE!90 #VALUE!92 #VALUE!

0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

Plot of price, delta, gamma, vega, theta or rhovs stock price for Black-Scholes model

94 #VALUE!96 #VALUE!98 #VALUE!

100 #VALUE!

0->Price, 1->Delta, 2->Gamma, 3->Vega, 4->Theta, 5->Rho

Strike40 50 60

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

Plot of price, delta, gamma, vega, theta or rhovs time to maturity for Black-Scholes model

40

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60

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.0000

2.0000

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10.0000

12.0000

Plot of price, delta, gamma, vega, theta or rhovs time to maturity for Black-Scholes model

40

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INVESTIGATES THE EFFECTIVENESS OF DELTA HEDGING FOR A WRITTEN OPTIONSee Tables 17.2 and 17.3 in Options, Futures, and Other Derivatives, 7e (and Tables 15.2 and 15.3 in Fundamentals, 6e)Uses Monte Carlo Simulation with the antithetic variable technique so that two trials are generated when F9 is pressed

Problem 17.30 in Options, Futures, and Other Derivatives, 7e (and 15.28 in Fundamentals, 6e) is based on this application

Hedging a call option - Table 13.2 Push F9 to see a new set of results

Stock Price 50 Weekly HedgingInt. Rate 0.05 Cum. Cost Payoff Tot. Cost

Vol 0.2 Base Case #VALUE! 0 #VALUE!Strike 50 Antithetic Case #VALUE! 156,985 #VALUE!

Number of Shares 100,000T 0.383562 Daily Hedging

IsCall 1 Cum. Cost Payoff Tot. CostBase Case #VALUE! 91,004 #VALUE!

Option Price #VALUE! Antithetic Case #VALUE! 24,914 #VALUE!

Base Case

Random Numbers Week T Delta Cost

Uniform Normal 0 0.000 50.00 #VALUE! #VALUE! #VALUE!0.31348 -0.48600 1 0.019 49.36 #VALUE! #VALUE! #VALUE!0.66748 0.43296 2 0.038 49.98 #VALUE! #VALUE! #VALUE!0.65384 0.39571 3 0.058 50.56 #VALUE! #VALUE! #VALUE!0.65039 0.38638 4 0.077 51.14 #VALUE! #VALUE! #VALUE!0.90780 1.32730 5 0.096 53.08 #VALUE! #VALUE! #VALUE!0.21529 -0.78820 6 0.115 51.97 #VALUE! #VALUE! #VALUE!0.74061 0.64521 7 0.134 52.93 #VALUE! #VALUE! #VALUE!0.27952 -0.58428 8 0.153 52.11 #VALUE! #VALUE! #VALUE!0.38683 -0.28758 9 0.173 51.73 #VALUE! #VALUE! #VALUE!0.57016 0.17679 10 0.192 52.01 #VALUE! #VALUE! #VALUE!0.49544 -0.01142 11 0.211 52.03 #VALUE! #VALUE! #VALUE!0.45708 -0.10778 12 0.230 51.90 #VALUE! #VALUE! #VALUE!0.46627 -0.08464 13 0.249 51.81 #VALUE! #VALUE! #VALUE!0.41413 -0.21693 14 0.268 51.53 #VALUE! #VALUE! #VALUE!0.37628 -0.31527 15 0.288 51.11 #VALUE! #VALUE! #VALUE!0.84870 1.03087 16 0.307 52.62 #VALUE! #VALUE! #VALUE!0.31726 -0.47537 17 0.326 51.96 #VALUE! #VALUE! #VALUE!0.09835 -1.29099 18 0.345 50.17 #VALUE! #VALUE! #VALUE!0.51555 0.03899 19 0.364 50.25 #VALUE! #VALUE! #VALUE!0.31284 -0.48782 20 0.383 49.61 #VALUE! #VALUE! #VALUE!

Base Case

Random Numbers Day T Delta Cost

Uniform Normal 0 0.000 50.00 #VALUE! #VALUE! #VALUE!0.50521 0.01307 1 0.003 50.01 #VALUE! #VALUE! #VALUE!0.28462 -0.56919 2 0.005 49.72 #VALUE! #VALUE! #VALUE!0.24147 -0.70158 3 0.008 49.36 #VALUE! #VALUE! #VALUE!

Stock Price

Shares Purchased

Stock Price

Shares Purchased

0.85394 1.05348 4 0.011 49.91 #VALUE! #VALUE! #VALUE!0.65101 0.38804 5 0.014 50.12 #VALUE! #VALUE! #VALUE!0.21653 -0.78396 6 0.016 49.71 #VALUE! #VALUE! #VALUE!0.55917 0.14887 7 0.019 49.79 #VALUE! #VALUE! #VALUE!0.35034 -0.38441 8 0.022 49.60 #VALUE! #VALUE! #VALUE!0.39944 -0.25481 9 0.025 49.47 #VALUE! #VALUE! #VALUE!0.37067 -0.33008 10 0.027 49.30 #VALUE! #VALUE! #VALUE!0.61888 0.30254 11 0.030 49.46 #VALUE! #VALUE! #VALUE!0.68522 0.48233 12 0.033 49.72 #VALUE! #VALUE! #VALUE!0.85486 1.05752 13 0.036 50.27 #VALUE! #VALUE! #VALUE!0.43090 -0.17409 14 0.038 50.19 #VALUE! #VALUE! #VALUE!0.13397 -1.10784 15 0.041 49.61 #VALUE! #VALUE! #VALUE!0.45993 -0.10062 16 0.044 49.56 #VALUE! #VALUE! #VALUE!0.93246 1.49434 17 0.047 50.35 #VALUE! #VALUE! #VALUE!0.14325 -1.06581 18 0.049 49.80 #VALUE! #VALUE! #VALUE!0.52401 0.06023 19 0.052 49.83 #VALUE! #VALUE! #VALUE!0.84876 1.03112 20 0.055 50.38 #VALUE! #VALUE! #VALUE!0.34351 -0.40291 21 0.058 50.17 #VALUE! #VALUE! #VALUE!0.61068 0.28109 22 0.060 50.32 #VALUE! #VALUE! #VALUE!0.46061 -0.09890 23 0.063 50.27 #VALUE! #VALUE! #VALUE!0.45677 -0.10858 24 0.066 50.22 #VALUE! #VALUE! #VALUE!0.28832 -0.55830 25 0.068 49.93 #VALUE! #VALUE! #VALUE!0.50863 0.02163 26 0.071 49.95 #VALUE! #VALUE! #VALUE!0.34742 -0.39231 27 0.074 49.75 #VALUE! #VALUE! #VALUE!0.02206 -2.01286 28 0.077 48.71 #VALUE! #VALUE! #VALUE!0.45733 -0.10716 29 0.079 48.66 #VALUE! #VALUE! #VALUE!0.98395 2.14314 30 0.082 49.77 #VALUE! #VALUE! #VALUE!0.87155 1.13375 31 0.085 50.37 #VALUE! #VALUE! #VALUE!0.46817 -0.07986 32 0.088 50.33 #VALUE! #VALUE! #VALUE!0.58622 0.21784 33 0.090 50.45 #VALUE! #VALUE! #VALUE!0.75023 0.67521 34 0.093 50.81 #VALUE! #VALUE! #VALUE!0.39902 -0.25588 35 0.096 50.68 #VALUE! #VALUE! #VALUE!0.01575 -2.15070 36 0.099 49.56 #VALUE! #VALUE! #VALUE!0.97500 1.96000 37 0.101 50.59 #VALUE! #VALUE! #VALUE!0.15831 -1.00143 38 0.104 50.06 #VALUE! #VALUE! #VALUE!0.37872 -0.30883 39 0.107 49.91 #VALUE! #VALUE! #VALUE!0.44900 -0.12818 40 0.110 49.84 #VALUE! #VALUE! #VALUE!0.40109 -0.25052 41 0.112 49.72 #VALUE! #VALUE! #VALUE!0.40308 -0.24539 42 0.115 49.59 #VALUE! #VALUE! #VALUE!0.99322 2.46869 43 0.118 50.90 #VALUE! #VALUE! #VALUE!0.30076 -0.52220 44 0.121 50.62 #VALUE! #VALUE! #VALUE!0.11140 -1.21912 45 0.123 49.98 #VALUE! #VALUE! #VALUE!0.81190 0.88491 46 0.126 50.45 #VALUE! #VALUE! #VALUE!0.41278 -0.22040 47 0.129 50.34 #VALUE! #VALUE! #VALUE!0.26953 -0.61423 48 0.132 50.02 #VALUE! #VALUE! #VALUE!0.01369 -2.20616 49 0.134 48.89 #VALUE! #VALUE! #VALUE!0.14512 -1.05758 50 0.137 48.35 #VALUE! #VALUE! #VALUE!0.35370 -0.37536 51 0.140 48.17 #VALUE! #VALUE! #VALUE!0.71699 0.57394 52 0.142 48.46 #VALUE! #VALUE! #VALUE!0.17383 -0.93914 53 0.145 47.99 #VALUE! #VALUE! #VALUE!0.95516 1.69710 54 0.148 48.85 #VALUE! #VALUE! #VALUE!0.97911 2.03576 55 0.151 49.91 #VALUE! #VALUE! #VALUE!0.75769 0.69890 56 0.153 50.28 #VALUE! #VALUE! #VALUE!0.71488 0.56770 57 0.156 50.58 #VALUE! #VALUE! #VALUE!

0.57984 0.20150 58 0.159 50.70 #VALUE! #VALUE! #VALUE!0.37489 -0.31894 59 0.162 50.53 #VALUE! #VALUE! #VALUE!0.83386 0.96955 60 0.164 51.05 #VALUE! #VALUE! #VALUE!0.49094 -0.02271 61 0.167 51.04 #VALUE! #VALUE! #VALUE!0.91193 1.35273 62 0.170 51.77 #VALUE! #VALUE! #VALUE!0.04822 -1.66234 63 0.173 50.89 #VALUE! #VALUE! #VALUE!0.72986 0.61237 64 0.175 51.22 #VALUE! #VALUE! #VALUE!0.48547 -0.03643 65 0.178 51.20 #VALUE! #VALUE! #VALUE!0.45192 -0.12081 66 0.181 51.14 #VALUE! #VALUE! #VALUE!0.55707 0.14355 67 0.184 51.22 #VALUE! #VALUE! #VALUE!0.63340 0.34087 68 0.186 51.41 #VALUE! #VALUE! #VALUE!0.12781 -1.13679 69 0.189 50.81 #VALUE! #VALUE! #VALUE!0.94761 1.62209 70 0.192 51.68 #VALUE! #VALUE! #VALUE!0.91814 1.39264 71 0.195 52.44 #VALUE! #VALUE! #VALUE!0.36634 -0.34156 72 0.197 52.26 #VALUE! #VALUE! #VALUE!0.19178 -0.87135 73 0.200 51.79 #VALUE! #VALUE! #VALUE!0.03414 -1.82322 74 0.203 50.82 #VALUE! #VALUE! #VALUE!0.44515 -0.13792 75 0.205 50.75 #VALUE! #VALUE! #VALUE!0.26549 -0.62651 76 0.208 50.42 #VALUE! #VALUE! #VALUE!0.73293 0.62168 77 0.211 50.75 #VALUE! #VALUE! #VALUE!0.25644 -0.65435 78 0.214 50.41 #VALUE! #VALUE! #VALUE!0.25281 -0.66568 79 0.216 50.06 #VALUE! #VALUE! #VALUE!0.14788 -1.04558 80 0.219 49.52 #VALUE! #VALUE! #VALUE!0.21568 -0.78687 81 0.222 49.12 #VALUE! #VALUE! #VALUE!0.39176 -0.27473 82 0.225 48.98 #VALUE! #VALUE! #VALUE!0.69059 0.49752 83 0.227 49.24 #VALUE! #VALUE! #VALUE!0.13667 -1.09539 84 0.230 48.69 #VALUE! #VALUE! #VALUE!0.34034 -0.41154 85 0.233 48.48 #VALUE! #VALUE! #VALUE!0.03490 -1.81316 86 0.236 47.57 #VALUE! #VALUE! #VALUE!0.90766 1.32647 87 0.238 48.24 #VALUE! #VALUE! #VALUE!0.68020 0.46827 88 0.241 48.48 #VALUE! #VALUE! #VALUE!0.58519 0.21519 89 0.244 48.60 #VALUE! #VALUE! #VALUE!0.10803 -1.23709 90 0.247 47.98 #VALUE! #VALUE! #VALUE!0.60408 0.26392 91 0.249 48.11 #VALUE! #VALUE! #VALUE!0.07222 -1.45944 92 0.252 47.39 #VALUE! #VALUE! #VALUE!0.76253 0.71447 93 0.255 47.75 #VALUE! #VALUE! #VALUE!0.68116 0.47096 94 0.258 47.99 #VALUE! #VALUE! #VALUE!0.33315 -0.43124 95 0.260 47.77 #VALUE! #VALUE! #VALUE!0.37877 -0.30870 96 0.263 47.62 #VALUE! #VALUE! #VALUE!0.68588 0.48420 97 0.266 47.87 #VALUE! #VALUE! #VALUE!0.36822 -0.33657 98 0.268 47.70 #VALUE! #VALUE! #VALUE!0.81744 0.90565 99 0.271 48.16 #VALUE! #VALUE! #VALUE!0.05527 -1.59577 100 0.274 47.37 #VALUE! #VALUE! #VALUE!0.97974 2.04838 101 0.277 48.40 #VALUE! #VALUE! #VALUE!0.28032 -0.58188 102 0.279 48.11 #VALUE! #VALUE! #VALUE!0.93525 1.51606 103 0.282 48.88 #VALUE! #VALUE! #VALUE!0.47391 -0.06545 104 0.285 48.85 #VALUE! #VALUE! #VALUE!0.95103 1.65497 105 0.288 49.71 #VALUE! #VALUE! #VALUE!0.09786 -1.29383 106 0.290 49.05 #VALUE! #VALUE! #VALUE!0.61086 0.28157 107 0.293 49.20 #VALUE! #VALUE! #VALUE!0.63079 0.33394 108 0.296 49.37 #VALUE! #VALUE! #VALUE!0.22099 -0.76886 109 0.299 48.98 #VALUE! #VALUE! #VALUE!0.09756 -1.29561 110 0.301 48.32 #VALUE! #VALUE! #VALUE!0.06307 -1.52948 111 0.304 47.56 #VALUE! #VALUE! #VALUE!

0.86425 1.09960 112 0.307 48.12 #VALUE! #VALUE! #VALUE!0.16484 -0.97477 113 0.310 47.63 #VALUE! #VALUE! #VALUE!0.32313 -0.45895 114 0.312 47.41 #VALUE! #VALUE! #VALUE!0.60176 0.25791 115 0.315 47.54 #VALUE! #VALUE! #VALUE!0.31745 -0.47485 116 0.318 47.31 #VALUE! #VALUE! #VALUE!0.88242 1.18715 117 0.321 47.90 #VALUE! #VALUE! #VALUE!0.95794 1.72724 118 0.323 48.78 #VALUE! #VALUE! #VALUE!0.94466 1.59515 119 0.326 49.61 #VALUE! #VALUE! #VALUE!0.98892 2.28748 120 0.329 50.81 #VALUE! #VALUE! #VALUE!0.67013 0.44027 121 0.332 51.05 #VALUE! #VALUE! #VALUE!0.03515 -1.80993 122 0.334 50.10 #VALUE! #VALUE! #VALUE!0.33591 -0.42364 123 0.337 49.88 #VALUE! #VALUE! #VALUE!0.86161 1.08758 124 0.340 50.46 #VALUE! #VALUE! #VALUE!0.91197 1.35300 125 0.342 51.18 #VALUE! #VALUE! #VALUE!0.08966 -1.34282 126 0.345 50.47 #VALUE! #VALUE! #VALUE!0.60775 0.27346 127 0.348 50.62 #VALUE! #VALUE! #VALUE!0.78888 0.80254 128 0.351 51.05 #VALUE! #VALUE! #VALUE!0.77062 0.74089 129 0.353 51.45 #VALUE! #VALUE! #VALUE!0.65752 0.40572 130 0.356 51.67 #VALUE! #VALUE! #VALUE!0.14500 -1.05814 131 0.359 51.11 #VALUE! #VALUE! #VALUE!0.32103 -0.46481 132 0.362 50.86 #VALUE! #VALUE! #VALUE!0.41125 -0.22433 133 0.364 50.75 #VALUE! #VALUE! #VALUE!0.49193 -0.02022 134 0.367 50.74 #VALUE! #VALUE! #VALUE!0.23344 -0.72755 135 0.370 50.36 #VALUE! #VALUE! #VALUE!0.48033 -0.04933 136 0.373 50.34 #VALUE! #VALUE! #VALUE!0.56472 0.16294 137 0.375 50.43 #VALUE! #VALUE! #VALUE!0.94257 1.57676 138 0.378 51.27 #VALUE! #VALUE! #VALUE!0.45876 -0.10357 139 0.381 51.22 #VALUE! #VALUE! #VALUE!0.27314 -0.60334 140 0.383 50.91 #VALUE! #VALUE! #VALUE!

INVESTIGATES THE EFFECTIVENESS OF DELTA HEDGING FOR A WRITTEN OPTIONSee Tables 17.2 and 17.3 in Options, Futures, and Other Derivatives, 7e (and Tables 15.2 and 15.3 in Fundamentals, 6e)Uses Monte Carlo Simulation with the antithetic variable technique so that two trials are generated when F9 is pressed

Problem 17.30 in Options, Futures, and Other Derivatives, 7e (and 15.28 in Fundamentals, 6e) is based on this application

Number of shares traded#VALUE!#VALUE!

Number of shares traded#VALUE!#VALUE!

Base Case Antithetic Case

Int. Cost Delta Cost Int. Cost

#VALUE! #VALUE! 50.00 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.71 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.13 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.61 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.11 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 47.37 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.44 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 47.61 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.42 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.83 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.62 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.66 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.84 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.98 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.30 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.76 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.39 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.06 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.88 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.85 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! 51.57 #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE!

Base Case Antithetic Case

Int. Cost Delta Cost Int. Cost

#VALUE! #VALUE! 50.00 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.00 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.30 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.68 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Cum. Cost

Stock Price

Shares Purchased

Cum. Cost

Cum. Cost

Stock Price

Shares Purchased

Cum. Cost

#VALUE! #VALUE! 50.12 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.92 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.34 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.27 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.47 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.61 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.79 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.63 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.38 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.83 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.93 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.51 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.57 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.79 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.35 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.33 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.79 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.00 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.86 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.92 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.98 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.28 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.27 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.48 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.56 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.62 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.48 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.89 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.93 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.82 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.48 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.61 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.75 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.72 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.25 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.42 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.49 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.62 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.76 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.47 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.74 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.39 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.93 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.05 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.37 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.55 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.13 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.34 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.03 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.55 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.63 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.55 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.18 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.89 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! 49.79 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.96 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.46 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.47 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.78 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.64 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.33 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.35 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.42 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.35 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.18 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.77 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.93 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.23 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.41 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 48.85 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.80 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.88 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.21 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.89 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.23 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.59 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.15 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.58 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.73 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.47 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.06 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.29 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.30 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.57 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.32 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.20 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.89 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.75 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.56 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.17 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.91 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.15 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.33 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.06 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.26 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.76 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.65 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.52 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.84 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.02 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.06 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.17 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.87 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.72 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.54 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.96 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.68 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.53 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! 52.92 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.47 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.73 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.59 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.86 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 53.20 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 52.25 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.39 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.18 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.95 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.91 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 51.14 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.57 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.86 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.57 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.43 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.01 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.63 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.43 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.98 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.23 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.35 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.37 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.75 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.78 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 50.70 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.88 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! 49.93 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE! 50.25 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE!

Trading Volume

Base Antithetic

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

Trading Volume

Base Antithetic

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

INVESTIGATES THE EFFECTIVENESS OF DELTA AND GAMMA HEDGING FOR A WRITTEN OPTIONUses Monte Carlo Simulation with the antithetic variable technique so that two trials are generated when F9 is pressed

Problem 24.31 in Options, Futures, and Other Derivatives, 7e is based on this application

Hedging a binary option with a call option

Market Data Binary Option Hedging Call

Stock Price 49 Strike 52 Strike 55Int. Rate 5% Number of Shares 1,000 T 0.5

Vol 30% T 0.3836 IsCall 1IsCall 1

IsCash 0Option Price #VALUE! Option Price #VALUE!

Base CaseAsset or Nothing Hedge Option

Random Numbers Week T Delta Gamma Price Delta

Uniform Normal 0 0.000 49.00 #VALUE! #VALUE! #VALUE! #VALUE!0.65887 0.40939 1 0.019 49.85 #VALUE! #VALUE! #VALUE! #VALUE!0.35028 -0.38456 2 0.038 49.06 #VALUE! #VALUE! #VALUE! #VALUE!0.84419 1.01183 3 0.058 51.17 #VALUE! #VALUE! #VALUE! #VALUE!0.22572 -0.75301 4 0.077 49.60 #VALUE! #VALUE! #VALUE! #VALUE!0.52274 0.05703 5 0.096 49.72 #VALUE! #VALUE! #VALUE! #VALUE!0.35421 -0.37398 6 0.115 48.96 #VALUE! #VALUE! #VALUE! #VALUE!0.42219 -0.19631 7 0.134 48.57 #VALUE! #VALUE! #VALUE! #VALUE!0.81449 0.89455 8 0.153 50.41 #VALUE! #VALUE! #VALUE! #VALUE!0.01219 -2.25114 9 0.173 45.91 #VALUE! #VALUE! #VALUE! #VALUE!0.78576 0.79181 10 0.192 47.45 #VALUE! #VALUE! #VALUE! #VALUE!0.69450 0.50865 11 0.211 48.47 #VALUE! #VALUE! #VALUE! #VALUE!0.84707 1.02395 12 0.230 50.58 #VALUE! #VALUE! #VALUE! #VALUE!0.76406 0.71942 13 0.249 52.12 #VALUE! #VALUE! #VALUE! #VALUE!0.98417 2.14874 14 0.268 57.00 #VALUE! #VALUE! #VALUE! #VALUE!0.71509 0.56832 15 0.288 58.36 #VALUE! #VALUE! #VALUE! #VALUE!0.67547 0.45508 16 0.307 59.48 #VALUE! #VALUE! #VALUE! #VALUE!0.13440 -1.10581 17 0.326 56.82 #VALUE! #VALUE! #VALUE! #VALUE!0.10384 -1.25996 18 0.345 53.93 #VALUE! #VALUE! #VALUE! #VALUE!0.38206 -0.30007 19 0.364 53.26 #VALUE! #VALUE! #VALUE! #VALUE!0.22738 -0.74750 20 0.383 51.64 #VALUE! #VALUE! #VALUE! #VALUE!

Antithetic CaseAsset or Nothing Hedge Option

Week T Delta Gamma Price Delta0 0.000 49.00 #VALUE! #VALUE! #VALUE! #VALUE!1 0.019 48.18 #VALUE! #VALUE! #VALUE! #VALUE!

Stock Price

Stock Price

2 0.038 48.96 #VALUE! #VALUE! #VALUE! #VALUE!3 0.058 46.95 #VALUE! #VALUE! #VALUE! #VALUE!4 0.077 48.44 #VALUE! #VALUE! #VALUE! #VALUE!5 0.096 48.33 #VALUE! #VALUE! #VALUE! #VALUE!6 0.115 49.10 #VALUE! #VALUE! #VALUE! #VALUE!7 0.134 49.50 #VALUE! #VALUE! #VALUE! #VALUE!8 0.153 47.70 #VALUE! #VALUE! #VALUE! #VALUE!9 0.173 52.38 #VALUE! #VALUE! #VALUE! #VALUE!

10 0.192 50.69 #VALUE! #VALUE! #VALUE! #VALUE!11 0.211 49.64 #VALUE! #VALUE! #VALUE! #VALUE!12 0.230 47.57 #VALUE! #VALUE! #VALUE! #VALUE!13 0.249 46.18 #VALUE! #VALUE! #VALUE! #VALUE!14 0.268 42.24 #VALUE! #VALUE! #VALUE! #VALUE!15 0.288 41.26 #VALUE! #VALUE! #VALUE! #VALUE!16 0.307 40.49 #VALUE! #VALUE! #VALUE! #VALUE!17 0.326 42.40 #VALUE! #VALUE! #VALUE! #VALUE!18 0.345 44.68 #VALUE! #VALUE! #VALUE! #VALUE!19 0.364 45.24 #VALUE! #VALUE! #VALUE! #VALUE!20 0.383 46.67 #VALUE! #VALUE! #VALUE! #VALUE!

INVESTIGATES THE EFFECTIVENESS OF DELTA AND GAMMA HEDGING FOR A WRITTEN OPTIONUses Monte Carlo Simulation with the antithetic variable technique so that two trials are generated when F9 is pressed

Problem 24.31 in Options, Futures, and Other Derivatives, 7e is based on this application

Push F9 to see a new set of results

Weekly Hedging Trading Volume

Cum. Cost Payoff Tot. Cost Calls SharesBase Case #VALUE! 0 #VALUE! #VALUE! #VALUE!

Antithetic Case #VALUE! 0 #VALUE! #VALUE! #VALUE!

Base CaseHedge Option Gamma Hedge Delta Hedge

Gamma Opt. Posn. Cost Net Delta Cost Total Cost Int. Cost

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Antithetic CaseHedge Option Gamma Hedge Delta Hedge

Gamma Opt. Posn. Cost Net Delta Cost Total Cost Int. Cost#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Opt. Purch.

Shares Purchased

Opt. Purch.

Shares Purchased

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Base CaseTrading Volume

Cum. Cost Calls Shares

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

Antithetic CaseTrading Volume

Cum. Cost Calls Shares#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE!

VALUE AT RISK CALCULATION FOR PORTFOLIO OF OPTIONS DEPENDENT ON A SINGLE STOCKUses Results in Chapter 20 of Options, Futures and Other Derivatives, 7e

Problem 20.21 in Options, Futures and Other Derivatives, 7e is based on this application

Today 0S 49 Portfolio

IsFut 0 Underlyingr 5% Black Scholesq 0% Black Scholes

Volatility 30% Black Scholes1-Day Vol 1.89%

PortfolioValue #VALUE!Delta #VALUE!

Gamma #VALUE!

Linear model 1-Day VaR #VALUE!

Quadratic Model E(dP) #VALUE! mu_P ###E(dp^2) #VALUE! Sig_P ###E(dP^3) #VALUE! Xi_P ###

1-Day VaR #VALUE!

Analytic VaR We calculate the analytic VaR by generating 1000 equally likely portfolio values1-Day VaR #VALUE!

PortfolioProb<S S Value

0.001 46.13840484 #VALUE!0.002 46.33478493 #VALUE!0.003 46.45551883 #VALUE!0.004 46.54414899 #VALUE!0.005 46.61474869 #VALUE!0.006 46.6737218 #VALUE!0.007 46.72454226 #VALUE!0.008 46.76931299 #VALUE!0.009 46.80940696 #VALUE!

0.01 46.84577172 #VALUE!0.011 46.87908966 #VALUE!0.012 46.90986907 #VALUE!0.013 46.93849905 #VALUE!0.014 46.96528434 #VALUE!0.015 46.99046819 #VALUE!0.016 47.01424798 #VALUE!0.017 47.03678614 #VALUE!0.018 47.05821803 #VALUE!0.019 47.07865763 #VALUE!

0.02 47.09820189 #VALUE!0.021 47.11693399 #VALUE!0.022 47.13492581 #VALUE!0.023 47.15223994 #VALUE!0.024 47.16893121 #VALUE!

45 46 47 48 49 50 51 52 530

2

4

6

8

10

12

Asset Price

Po

rtfo

lio

Val

ue

0.025 47.18504795 #VALUE!0.026 47.20063297 #VALUE!0.027 47.21572436 #VALUE!0.028 47.23035623 #VALUE!0.029 47.24455916 #VALUE!

0.03 47.25836075 #VALUE!0.031 47.27178596 #VALUE!0.032 47.28485745 #VALUE!0.033 47.29759586 #VALUE!0.034 47.31002003 #VALUE!0.035 47.32214724 #VALUE!0.036 47.33399332 #VALUE!0.037 47.34557287 #VALUE!0.038 47.35689936 #VALUE!0.039 47.36798523 #VALUE!

0.04 47.37884201 #VALUE!0.041 47.38948042 #VALUE!0.042 47.39991043 #VALUE!0.043 47.4101413 #VALUE!0.044 47.42018171 #VALUE!0.045 47.43003975 #VALUE!0.046 47.43972301 #VALUE!0.047 47.44923861 #VALUE!0.048 47.45859322 #VALUE!0.049 47.46779312 #VALUE!

0.05 47.47684423 #VALUE!0.051 47.48575211 #VALUE!0.052 47.49452204 #VALUE!0.053 47.50315897 #VALUE!0.054 47.51166762 #VALUE!0.055 47.52005244 #VALUE!0.056 47.52831765 #VALUE!0.057 47.53646725 #VALUE!0.058 47.54450504 #VALUE!0.059 47.55243465 #VALUE!

0.06 47.5602595 #VALUE!0.061 47.56798289 #VALUE!0.062 47.57560792 #VALUE!0.063 47.58313759 #VALUE!0.064 47.59057472 #VALUE!0.065 47.59792203 #VALUE!0.066 47.60518212 #VALUE!0.067 47.61235748 #VALUE!0.068 47.61945047 #VALUE!0.069 47.62646338 #VALUE!

0.07 47.63339838 #VALUE!0.071 47.64025757 #VALUE!0.072 47.64704296 #VALUE!0.073 47.65375647 #VALUE!0.074 47.66039996 #VALUE!0.075 47.6669752 #VALUE!0.076 47.67348392 #VALUE!0.077 47.67992775 #VALUE!0.078 47.68630828 #VALUE!

0.079 47.69262705 #VALUE!0.08 47.69888553 #VALUE!

0.081 47.70508513 #VALUE!0.082 47.71122722 #VALUE!0.083 47.71731314 #VALUE!0.084 47.72334415 #VALUE!0.085 47.72932149 #VALUE!0.086 47.73524635 #VALUE!0.087 47.74111988 #VALUE!0.088 47.7469432 #VALUE!0.089 47.75271738 #VALUE!

0.09 47.75844346 #VALUE!0.091 47.76412247 #VALUE!0.092 47.76975537 #VALUE!0.093 47.77534311 #VALUE!0.094 47.78088661 #VALUE!0.095 47.78638676 #VALUE!0.096 47.79184443 #VALUE!0.097 47.79726045 #VALUE!0.098 47.80263563 #VALUE!0.099 47.80797078 #VALUE!

0.1 47.81326664 #VALUE!0.101 47.81852398 #VALUE!0.102 47.8237435 #VALUE!0.103 47.82892592 #VALUE!0.104 47.83407192 #VALUE!0.105 47.83918216 #VALUE!0.106 47.84425729 #VALUE!0.107 47.84929794 #VALUE!0.108 47.85430473 #VALUE!0.109 47.85927824 #VALUE!

0.11 47.86421907 #VALUE!0.111 47.86912777 #VALUE!0.112 47.87400489 #VALUE!0.113 47.87885099 #VALUE!0.114 47.88366656 #VALUE!0.115 47.88845214 #VALUE!0.116 47.89320822 #VALUE!0.117 47.89793527 #VALUE!0.118 47.90263378 #VALUE!0.119 47.90730421 #VALUE!

0.12 47.911947 #VALUE!0.121 47.91656261 #VALUE!0.122 47.92115145 #VALUE!0.123 47.92571395 #VALUE!0.124 47.93025053 #VALUE!0.125 47.93476157 #VALUE!0.126 47.93924747 #VALUE!0.127 47.94370861 #VALUE!0.128 47.94814538 #VALUE!0.129 47.95255813 #VALUE!

0.13 47.95694722 #VALUE!0.131 47.961313 #VALUE!0.132 47.96565582 #VALUE!

0.133 47.969976 #VALUE!0.134 47.97427388 #VALUE!0.135 47.97854978 #VALUE!0.136 47.98280401 #VALUE!0.137 47.98703688 #VALUE!0.138 47.99124868 #VALUE!0.139 47.99543973 #VALUE!

0.14 47.99961029 #VALUE!0.141 48.00376066 #VALUE!0.142 48.00789112 #VALUE!0.143 48.01200193 #VALUE!0.144 48.01609336 #VALUE!0.145 48.02016567 #VALUE!0.146 48.02421912 #VALUE!0.147 48.02825396 #VALUE!0.148 48.03227044 #VALUE!0.149 48.03626879 #VALUE!

0.15 48.04024925 #VALUE!0.151 48.04421206 #VALUE!0.152 48.04815744 #VALUE!0.153 48.05208562 #VALUE!0.154 48.05599681 #VALUE!0.155 48.05989124 #VALUE!0.156 48.06376911 #VALUE!0.157 48.06763063 #VALUE!0.158 48.071476 #VALUE!0.159 48.07530543 #VALUE!

0.16 48.07911911 #VALUE!0.161 48.08291724 #VALUE!0.162 48.0867 #VALUE!0.163 48.09046758 #VALUE!0.164 48.09422016 #VALUE!0.165 48.09795793 #VALUE!0.166 48.10168105 #VALUE!0.167 48.10538972 #VALUE!0.168 48.10908409 #VALUE!0.169 48.11276433 #VALUE!

0.17 48.11643061 #VALUE!0.171 48.12008309 #VALUE!0.172 48.12372194 #VALUE!0.173 48.1273473 #VALUE!0.174 48.13095934 #VALUE!0.175 48.13455821 #VALUE!0.176 48.13814404 #VALUE!0.177 48.14171701 #VALUE!0.178 48.14527724 #VALUE!0.179 48.14882488 #VALUE!

0.18 48.15236007 #VALUE!0.181 48.15588295 #VALUE!0.182 48.15939365 #VALUE!0.183 48.16289232 #VALUE!0.184 48.16637907 #VALUE!0.185 48.16985405 #VALUE!0.186 48.17331737 #VALUE!

0.187 48.17676917 #VALUE!0.188 48.18020957 #VALUE!0.189 48.18363869 #VALUE!

0.19 48.18705665 #VALUE!0.191 48.19046358 #VALUE!0.192 48.19385958 #VALUE!0.193 48.19724477 #VALUE!0.194 48.20061927 #VALUE!0.195 48.20398318 #VALUE!0.196 48.20733662 #VALUE!0.197 48.21067971 #VALUE!0.198 48.21401253 #VALUE!0.199 48.2173352 #VALUE!

0.2 48.22064783 #VALUE!0.201 48.22395052 #VALUE!0.202 48.22724336 #VALUE!0.203 48.23052646 #VALUE!0.204 48.23379991 #VALUE!0.205 48.23706382 #VALUE!0.206 48.24031828 #VALUE!0.207 48.24356338 #VALUE!0.208 48.24679922 #VALUE!0.209 48.25002589 #VALUE!

0.21 48.25324347 #VALUE!0.211 48.25645207 #VALUE!0.212 48.25965177 #VALUE!0.213 48.26284265 #VALUE!0.214 48.2660248 #VALUE!0.215 48.2691983 #VALUE!0.216 48.27236325 #VALUE!0.217 48.27551972 #VALUE!0.218 48.27866779 #VALUE!0.219 48.28180755 #VALUE!

0.22 48.28493908 #VALUE!0.221 48.28806245 #VALUE!0.222 48.29117774 #VALUE!0.223 48.29428502 #VALUE!0.224 48.29738439 #VALUE!0.225 48.3004759 #VALUE!0.226 48.30355963 #VALUE!0.227 48.30663566 #VALUE!0.228 48.30970406 #VALUE!0.229 48.3127649 #VALUE!

0.23 48.31581824 #VALUE!0.231 48.31886417 #VALUE!0.232 48.32190274 #VALUE!0.233 48.32493404 #VALUE!0.234 48.32795811 #VALUE!0.235 48.33097504 #VALUE!0.236 48.33398488 #VALUE!0.237 48.3369877 #VALUE!0.238 48.33998356 #VALUE!0.239 48.34297253 #VALUE!

0.24 48.34595467 #VALUE!

0.241 48.34893005 #VALUE!0.242 48.35189872 #VALUE!0.243 48.35486074 #VALUE!0.244 48.35781617 #VALUE!0.245 48.36076508 #VALUE!0.246 48.36370752 #VALUE!0.247 48.36664355 #VALUE!0.248 48.36957323 #VALUE!0.249 48.37249661 #VALUE!

0.25 48.37541375 #VALUE!0.251 48.37832471 #VALUE!0.252 48.38122953 #VALUE!0.253 48.38412828 #VALUE!0.254 48.387021 #VALUE!0.255 48.38990776 #VALUE!0.256 48.3927886 #VALUE!0.257 48.39566357 #VALUE!0.258 48.39853273 #VALUE!0.259 48.40139613 #VALUE!

0.26 48.40425382 #VALUE!0.261 48.40710584 #VALUE!0.262 48.40995225 #VALUE!0.263 48.4127931 #VALUE!0.264 48.41562843 #VALUE!0.265 48.41845829 #VALUE!0.266 48.42128273 #VALUE!0.267 48.4241018 #VALUE!0.268 48.42691554 #VALUE!0.269 48.429724 #VALUE!

0.27 48.43252723 #VALUE!0.271 48.43532526 #VALUE!0.272 48.43811815 #VALUE!0.273 48.44090594 #VALUE!0.274 48.44368866 #VALUE!0.275 48.44646638 #VALUE!0.276 48.44923912 #VALUE!0.277 48.45200693 #VALUE!0.278 48.45476986 #VALUE!0.279 48.45752794 #VALUE!

0.28 48.46028121 #VALUE!0.281 48.46302972 #VALUE!0.282 48.46577351 #VALUE!0.283 48.46851262 #VALUE!0.284 48.47124709 #VALUE!0.285 48.47397695 #VALUE!0.286 48.47670225 #VALUE!0.287 48.47942302 #VALUE!0.288 48.48213931 #VALUE!0.289 48.48485115 #VALUE!

0.29 48.48755858 #VALUE!0.291 48.49026163 #VALUE!0.292 48.49296035 #VALUE!0.293 48.49565477 #VALUE!0.294 48.49834493 #VALUE!

0.295 48.50103085 #VALUE!0.296 48.50371259 #VALUE!0.297 48.50639017 #VALUE!0.298 48.50906363 #VALUE!0.299 48.51173301 #VALUE!

0.3 48.51439833 #VALUE!0.301 48.51705964 #VALUE!0.302 48.51971696 #VALUE!0.303 48.52237033 #VALUE!0.304 48.52501979 #VALUE!0.305 48.52766537 #VALUE!0.306 48.5303071 #VALUE!0.307 48.532945 #VALUE!0.308 48.53557913 #VALUE!0.309 48.5382095 #VALUE!

0.31 48.54083615 #VALUE!0.311 48.54345911 #VALUE!0.312 48.54607842 #VALUE!0.313 48.5486941 #VALUE!0.314 48.55130618 #VALUE!0.315 48.55391469 #VALUE!0.316 48.55651968 #VALUE!0.317 48.55912115 #VALUE!0.318 48.56171915 #VALUE!0.319 48.56431371 #VALUE!

0.32 48.56690485 #VALUE!0.321 48.56949261 #VALUE!0.322 48.572077 #VALUE!0.323 48.57465807 #VALUE!0.324 48.57723584 #VALUE!0.325 48.57981033 #VALUE!0.326 48.58238158 #VALUE!0.327 48.58494962 #VALUE!0.328 48.58751447 #VALUE!0.329 48.59007615 #VALUE!

0.33 48.59263471 #VALUE!0.331 48.59519016 #VALUE!0.332 48.59774252 #VALUE!0.333 48.60029184 #VALUE!0.334 48.60283813 #VALUE!0.335 48.60538142 #VALUE!0.336 48.60792174 #VALUE!0.337 48.61045911 #VALUE!0.338 48.61299356 #VALUE!0.339 48.61552511 #VALUE!

0.34 48.6180538 #VALUE!0.341 48.62057964 #VALUE!0.342 48.62310265 #VALUE!0.343 48.62562288 #VALUE!0.344 48.62814033 #VALUE!0.345 48.63065504 #VALUE!0.346 48.63316703 #VALUE!0.347 48.63567632 #VALUE!0.348 48.63818294 #VALUE!

0.349 48.64068691 #VALUE!0.35 48.64318825 #VALUE!

0.351 48.645687 #VALUE!0.352 48.64818317 #VALUE!0.353 48.65067678 #VALUE!0.354 48.65316787 #VALUE!0.355 48.65565644 #VALUE!0.356 48.65814253 #VALUE!0.357 48.66062616 #VALUE!0.358 48.66310736 #VALUE!0.359 48.66558613 #VALUE!

0.36 48.66806251 #VALUE!0.361 48.67053652 #VALUE!0.362 48.67300818 #VALUE!0.363 48.67547751 #VALUE!0.364 48.67794454 #VALUE!0.365 48.68040929 #VALUE!0.366 48.68287177 #VALUE!0.367 48.68533201 #VALUE!0.368 48.68779003 #VALUE!0.369 48.69024585 #VALUE!

0.37 48.6926995 #VALUE!0.371 48.69515099 #VALUE!0.372 48.69760035 #VALUE!0.373 48.70004759 #VALUE!0.374 48.70249274 #VALUE!0.375 48.70493582 #VALUE!0.376 48.70737685 #VALUE!0.377 48.70981584 #VALUE!0.378 48.71225282 #VALUE!0.379 48.71468781 #VALUE!

0.38 48.71712083 #VALUE!0.381 48.7195519 #VALUE!0.382 48.72198104 #VALUE!0.383 48.72440826 #VALUE!0.384 48.7268336 #VALUE!0.385 48.72925706 #VALUE!0.386 48.73167867 #VALUE!0.387 48.73409844 #VALUE!0.388 48.7365164 #VALUE!0.389 48.73893257 #VALUE!

0.39 48.74134695 #VALUE!0.391 48.74375959 #VALUE!0.392 48.74617048 #VALUE!0.393 48.74857965 #VALUE!0.394 48.75098713 #VALUE!0.395 48.75339292 #VALUE!0.396 48.75579705 #VALUE!0.397 48.75819953 #VALUE!0.398 48.76060039 #VALUE!0.399 48.76299964 #VALUE!

0.4 48.7653973 #VALUE!0.401 48.76779339 #VALUE!0.402 48.77018792 #VALUE!

0.403 48.77258092 #VALUE!0.404 48.7749724 #VALUE!0.405 48.77736238 #VALUE!0.406 48.77975088 #VALUE!0.407 48.78213791 #VALUE!0.408 48.7845235 #VALUE!0.409 48.78690766 #VALUE!

0.41 48.7892904 #VALUE!0.411 48.79167175 #VALUE!0.412 48.79405173 #VALUE!0.413 48.79643035 #VALUE!0.414 48.79880762 #VALUE!0.415 48.80118357 #VALUE!0.416 48.80355821 #VALUE!0.417 48.80593155 #VALUE!0.418 48.80830363 #VALUE!0.419 48.81067445 #VALUE!

0.42 48.81304402 #VALUE!0.421 48.81541238 #VALUE!0.422 48.81777952 #VALUE!0.423 48.82014548 #VALUE!0.424 48.82251026 #VALUE!0.425 48.82487389 #VALUE!0.426 48.82723637 #VALUE!0.427 48.82959773 #VALUE!0.428 48.83195799 #VALUE!0.429 48.83431715 #VALUE!

0.43 48.83667524 #VALUE!0.431 48.83903227 #VALUE!0.432 48.84138825 #VALUE!0.433 48.84374321 #VALUE!0.434 48.84609716 #VALUE!0.435 48.84845012 #VALUE!0.436 48.8508021 #VALUE!0.437 48.85315312 #VALUE!0.438 48.85550319 #VALUE!0.439 48.85785232 #VALUE!

0.44 48.86020055 #VALUE!0.441 48.86254788 #VALUE!0.442 48.86489432 #VALUE!0.443 48.8672399 #VALUE!0.444 48.86958462 #VALUE!0.445 48.87192851 #VALUE!0.446 48.87427158 #VALUE!0.447 48.87661384 #VALUE!0.448 48.87895532 #VALUE!0.449 48.88129602 #VALUE!

0.45 48.88363596 #VALUE!0.451 48.88597516 #VALUE!0.452 48.88831364 #VALUE!0.453 48.8906514 #VALUE!0.454 48.89298846 #VALUE!0.455 48.89532485 #VALUE!0.456 48.89766056 #VALUE!

0.457 48.89999563 #VALUE!0.458 48.90233006 #VALUE!0.459 48.90466387 #VALUE!

0.46 48.90699707 #VALUE!0.461 48.90932969 #VALUE!0.462 48.91166173 #VALUE!0.463 48.9139932 #VALUE!0.464 48.91632414 #VALUE!0.465 48.91865454 #VALUE!0.466 48.92098443 #VALUE!0.467 48.92331382 #VALUE!0.468 48.92564272 #VALUE!0.469 48.92797115 #VALUE!

0.47 48.93029913 #VALUE!0.471 48.93262667 #VALUE!0.472 48.93495378 #VALUE!0.473 48.93728048 #VALUE!0.474 48.93960679 #VALUE!0.475 48.94193271 #VALUE!0.476 48.94425827 #VALUE!0.477 48.94658347 #VALUE!0.478 48.94890834 #VALUE!0.479 48.95123289 #VALUE!

0.48 48.95355713 #VALUE!0.481 48.95588108 #VALUE!0.482 48.95820475 #VALUE!0.483 48.96052816 #VALUE!0.484 48.96285131 #VALUE!0.485 48.96517424 #VALUE!0.486 48.96749694 #VALUE!0.487 48.96981944 #VALUE!0.488 48.97214176 #VALUE!0.489 48.97446389 #VALUE!

0.49 48.97678587 #VALUE!0.491 48.9791077 #VALUE!0.492 48.98142939 #VALUE!0.493 48.98375097 #VALUE!0.494 48.98607245 #VALUE!0.495 48.98839384 #VALUE!0.496 48.99071516 #VALUE!0.497 48.99303642 #VALUE!0.498 48.99535764 #VALUE!0.499 48.99767883 #VALUE!

0.5 49 #VALUE!0.501 49.00232117 #VALUE!0.502 49.00464236 #VALUE!0.503 49.00696358 #VALUE!0.504 49.00928484 #VALUE!0.505 49.01160616 #VALUE!0.506 49.01392755 #VALUE!0.507 49.01624903 #VALUE!0.508 49.01857061 #VALUE!0.509 49.0208923 #VALUE!

0.51 49.02321413 #VALUE!

0.511 49.02553611 #VALUE!0.512 49.02785824 #VALUE!0.513 49.03018056 #VALUE!0.514 49.03250306 #VALUE!0.515 49.03482576 #VALUE!0.516 49.03714869 #VALUE!0.517 49.03947184 #VALUE!0.518 49.04179525 #VALUE!0.519 49.04411892 #VALUE!

0.52 49.04644287 #VALUE!0.521 49.04876711 #VALUE!0.522 49.05109166 #VALUE!0.523 49.05341653 #VALUE!0.524 49.05574173 #VALUE!0.525 49.05806729 #VALUE!0.526 49.06039321 #VALUE!0.527 49.06271952 #VALUE!0.528 49.06504622 #VALUE!0.529 49.06737333 #VALUE!

0.53 49.06970087 #VALUE!0.531 49.07202885 #VALUE!0.532 49.07435728 #VALUE!0.533 49.07668618 #VALUE!0.534 49.07901557 #VALUE!0.535 49.08134546 #VALUE!0.536 49.08367586 #VALUE!0.537 49.0860068 #VALUE!0.538 49.08833827 #VALUE!0.539 49.09067031 #VALUE!

0.54 49.09300293 #VALUE!0.541 49.09533613 #VALUE!0.542 49.09766994 #VALUE!0.543 49.10000437 #VALUE!0.544 49.10233944 #VALUE!0.545 49.10467515 #VALUE!0.546 49.10701154 #VALUE!0.547 49.1093486 #VALUE!0.548 49.11168636 #VALUE!0.549 49.11402484 #VALUE!

0.55 49.11636404 #VALUE!0.551 49.11870398 #VALUE!0.552 49.12104468 #VALUE!0.553 49.12338616 #VALUE!0.554 49.12572842 #VALUE!0.555 49.12807149 #VALUE!0.556 49.13041538 #VALUE!0.557 49.1327601 #VALUE!0.558 49.13510568 #VALUE!0.559 49.13745212 #VALUE!

0.56 49.13979945 #VALUE!0.561 49.14214768 #VALUE!0.562 49.14449681 #VALUE!0.563 49.14684688 #VALUE!0.564 49.1491979 #VALUE!

0.565 49.15154988 #VALUE!0.566 49.15390284 #VALUE!0.567 49.15625679 #VALUE!0.568 49.15861175 #VALUE!0.569 49.16096773 #VALUE!

0.57 49.16332476 #VALUE!0.571 49.16568285 #VALUE!0.572 49.16804201 #VALUE!0.573 49.17040227 #VALUE!0.574 49.17276363 #VALUE!0.575 49.17512611 #VALUE!0.576 49.17748974 #VALUE!0.577 49.17985452 #VALUE!0.578 49.18222048 #VALUE!0.579 49.18458762 #VALUE!

0.58 49.18695598 #VALUE!0.581 49.18932555 #VALUE!0.582 49.19169637 #VALUE!0.583 49.19406845 #VALUE!0.584 49.19644179 #VALUE!0.585 49.19881643 #VALUE!0.586 49.20119238 #VALUE!0.587 49.20356965 #VALUE!0.588 49.20594827 #VALUE!0.589 49.20832825 #VALUE!

0.59 49.2107096 #VALUE!0.591 49.21309234 #VALUE!0.592 49.2154765 #VALUE!0.593 49.21786209 #VALUE!0.594 49.22024912 #VALUE!0.595 49.22263762 #VALUE!0.596 49.2250276 #VALUE!0.597 49.22741908 #VALUE!0.598 49.22981208 #VALUE!0.599 49.23220661 #VALUE!

0.6 49.2346027 #VALUE!0.601 49.23700036 #VALUE!0.602 49.23939961 #VALUE!0.603 49.24180047 #VALUE!0.604 49.24420295 #VALUE!0.605 49.24660708 #VALUE!0.606 49.24901287 #VALUE!0.607 49.25142035 #VALUE!0.608 49.25382952 #VALUE!0.609 49.25624041 #VALUE!

0.61 49.25865305 #VALUE!0.611 49.26106743 #VALUE!0.612 49.2634836 #VALUE!0.613 49.26590156 #VALUE!0.614 49.26832133 #VALUE!0.615 49.27074294 #VALUE!0.616 49.2731664 #VALUE!0.617 49.27559174 #VALUE!0.618 49.27801896 #VALUE!

0.619 49.2804481 #VALUE!0.62 49.28287917 #VALUE!

0.621 49.28531219 #VALUE!0.622 49.28774718 #VALUE!0.623 49.29018416 #VALUE!0.624 49.29262315 #VALUE!0.625 49.29506418 #VALUE!0.626 49.29750726 #VALUE!0.627 49.29995241 #VALUE!0.628 49.30239965 #VALUE!0.629 49.30484901 #VALUE!

0.63 49.3073005 #VALUE!0.631 49.30975415 #VALUE!0.632 49.31220997 #VALUE!0.633 49.31466799 #VALUE!0.634 49.31712823 #VALUE!0.635 49.31959071 #VALUE!0.636 49.32205546 #VALUE!0.637 49.32452249 #VALUE!0.638 49.32699182 #VALUE!0.639 49.32946348 #VALUE!

0.64 49.33193749 #VALUE!0.641 49.33441387 #VALUE!0.642 49.33689264 #VALUE!0.643 49.33937384 #VALUE!0.644 49.34185747 #VALUE!0.645 49.34434356 #VALUE!0.646 49.34683213 #VALUE!0.647 49.34932322 #VALUE!0.648 49.35181683 #VALUE!0.649 49.354313 #VALUE!

0.65 49.35681175 #VALUE!0.651 49.35931309 #VALUE!0.652 49.36181706 #VALUE!0.653 49.36432368 #VALUE!0.654 49.36683297 #VALUE!0.655 49.36934496 #VALUE!0.656 49.37185967 #VALUE!0.657 49.37437712 #VALUE!0.658 49.37689735 #VALUE!0.659 49.37942036 #VALUE!

0.66 49.3819462 #VALUE!0.661 49.38447489 #VALUE!0.662 49.38700644 #VALUE!0.663 49.38954089 #VALUE!0.664 49.39207826 #VALUE!0.665 49.39461858 #VALUE!0.666 49.39716187 #VALUE!0.667 49.39970816 #VALUE!0.668 49.40225748 #VALUE!0.669 49.40480984 #VALUE!

0.67 49.40736529 #VALUE!0.671 49.40992385 #VALUE!0.672 49.41248553 #VALUE!

0.673 49.41505038 #VALUE!0.674 49.41761842 #VALUE!0.675 49.42018967 #VALUE!0.676 49.42276416 #VALUE!0.677 49.42534193 #VALUE!0.678 49.427923 #VALUE!0.679 49.43050739 #VALUE!

0.68 49.43309515 #VALUE!0.681 49.43568629 #VALUE!0.682 49.43828085 #VALUE!0.683 49.44087885 #VALUE!0.684 49.44348032 #VALUE!0.685 49.44608531 #VALUE!0.686 49.44869382 #VALUE!0.687 49.4513059 #VALUE!0.688 49.45392158 #VALUE!0.689 49.45654089 #VALUE!

0.69 49.45916385 #VALUE!0.691 49.4617905 #VALUE!0.692 49.46442087 #VALUE!0.693 49.467055 #VALUE!0.694 49.4696929 #VALUE!0.695 49.47233463 #VALUE!0.696 49.47498021 #VALUE!0.697 49.47762967 #VALUE!0.698 49.48028304 #VALUE!0.699 49.48294036 #VALUE!

0.7 49.48560167 #VALUE!0.701 49.48826699 #VALUE!0.702 49.49093637 #VALUE!0.703 49.49360983 #VALUE!0.704 49.49628741 #VALUE!0.705 49.49896915 #VALUE!0.706 49.50165507 #VALUE!0.707 49.50434523 #VALUE!0.708 49.50703965 #VALUE!0.709 49.50973837 #VALUE!

0.71 49.51244142 #VALUE!0.711 49.51514885 #VALUE!0.712 49.51786069 #VALUE!0.713 49.52057698 #VALUE!0.714 49.52329775 #VALUE!0.715 49.52602305 #VALUE!0.716 49.52875291 #VALUE!0.717 49.53148738 #VALUE!0.718 49.53422649 #VALUE!0.719 49.53697028 #VALUE!

0.72 49.53971879 #VALUE!0.721 49.54247206 #VALUE!0.722 49.54523014 #VALUE!0.723 49.54799307 #VALUE!0.724 49.55076088 #VALUE!0.725 49.55353362 #VALUE!0.726 49.55631134 #VALUE!

0.727 49.55909406 #VALUE!0.728 49.56188185 #VALUE!0.729 49.56467474 #VALUE!

0.73 49.56747277 #VALUE!0.731 49.570276 #VALUE!0.732 49.57308446 #VALUE!0.733 49.5758982 #VALUE!0.734 49.57871727 #VALUE!0.735 49.58154171 #VALUE!0.736 49.58437157 #VALUE!0.737 49.5872069 #VALUE!0.738 49.59004775 #VALUE!0.739 49.59289416 #VALUE!

0.74 49.59574618 #VALUE!0.741 49.59860387 #VALUE!0.742 49.60146727 #VALUE!0.743 49.60433643 #VALUE!0.744 49.6072114 #VALUE!0.745 49.61009224 #VALUE!0.746 49.612979 #VALUE!0.747 49.61587172 #VALUE!0.748 49.61877047 #VALUE!0.749 49.62167529 #VALUE!

0.75 49.62458625 #VALUE!0.751 49.62750339 #VALUE!0.752 49.63042677 #VALUE!0.753 49.63335645 #VALUE!0.754 49.63629248 #VALUE!0.755 49.63923492 #VALUE!0.756 49.64218383 #VALUE!0.757 49.64513926 #VALUE!0.758 49.64810128 #VALUE!0.759 49.65106995 #VALUE!

0.76 49.65404533 #VALUE!0.761 49.65702747 #VALUE!0.762 49.66001644 #VALUE!0.763 49.6630123 #VALUE!0.764 49.66601512 #VALUE!0.765 49.66902496 #VALUE!0.766 49.67204189 #VALUE!0.767 49.67506596 #VALUE!0.768 49.67809726 #VALUE!0.769 49.68113583 #VALUE!

0.77 49.68418176 #VALUE!0.771 49.6872351 #VALUE!0.772 49.69029594 #VALUE!0.773 49.69336434 #VALUE!0.774 49.69644037 #VALUE!0.775 49.6995241 #VALUE!0.776 49.70261561 #VALUE!0.777 49.70571498 #VALUE!0.778 49.70882226 #VALUE!0.779 49.71193755 #VALUE!

0.78 49.71506092 #VALUE!

0.781 49.71819245 #VALUE!0.782 49.72133221 #VALUE!0.783 49.72448028 #VALUE!0.784 49.72763675 #VALUE!0.785 49.7308017 #VALUE!0.786 49.7339752 #VALUE!0.787 49.73715735 #VALUE!0.788 49.74034823 #VALUE!0.789 49.74354793 #VALUE!

0.79 49.74675653 #VALUE!0.791 49.74997411 #VALUE!0.792 49.75320078 #VALUE!0.793 49.75643662 #VALUE!0.794 49.75968172 #VALUE!0.795 49.76293618 #VALUE!0.796 49.76620009 #VALUE!0.797 49.76947354 #VALUE!0.798 49.77275664 #VALUE!0.799 49.77604948 #VALUE!

0.8 49.77935217 #VALUE!0.801 49.7826648 #VALUE!0.802 49.78598747 #VALUE!0.803 49.78932029 #VALUE!0.804 49.79266338 #VALUE!0.805 49.79601682 #VALUE!0.806 49.79938073 #VALUE!0.807 49.80275523 #VALUE!0.808 49.80614042 #VALUE!0.809 49.80953642 #VALUE!

0.81 49.81294335 #VALUE!0.811 49.81636131 #VALUE!0.812 49.81979043 #VALUE!0.813 49.82323083 #VALUE!0.814 49.82668263 #VALUE!0.815 49.83014595 #VALUE!0.816 49.83362093 #VALUE!0.817 49.83710768 #VALUE!0.818 49.84060635 #VALUE!0.819 49.84411705 #VALUE!

0.82 49.84763993 #VALUE!0.821 49.85117512 #VALUE!0.822 49.85472276 #VALUE!0.823 49.85828299 #VALUE!0.824 49.86185596 #VALUE!0.825 49.86544179 #VALUE!0.826 49.86904066 #VALUE!0.827 49.8726527 #VALUE!0.828 49.87627806 #VALUE!0.829 49.87991691 #VALUE!

0.83 49.88356939 #VALUE!0.831 49.88723567 #VALUE!0.832 49.89091591 #VALUE!0.833 49.89461028 #VALUE!0.834 49.89831895 #VALUE!

0.835 49.90204207 #VALUE!0.836 49.90577984 #VALUE!0.837 49.90953242 #VALUE!0.838 49.9133 #VALUE!0.839 49.91708276 #VALUE!

0.84 49.92088089 #VALUE!0.841 49.92469457 #VALUE!0.842 49.928524 #VALUE!0.843 49.93236937 #VALUE!0.844 49.93623089 #VALUE!0.845 49.94010876 #VALUE!0.846 49.94400319 #VALUE!0.847 49.94791438 #VALUE!0.848 49.95184256 #VALUE!0.849 49.95578794 #VALUE!

0.85 49.95975075 #VALUE!0.851 49.96373121 #VALUE!0.852 49.96772956 #VALUE!0.853 49.97174604 #VALUE!0.854 49.97578088 #VALUE!0.855 49.97983433 #VALUE!0.856 49.98390664 #VALUE!0.857 49.98799807 #VALUE!0.858 49.99210888 #VALUE!0.859 49.99623934 #VALUE!

0.86 50.00038971 #VALUE!0.861 50.00456027 #VALUE!0.862 50.00875132 #VALUE!0.863 50.01296312 #VALUE!0.864 50.01719599 #VALUE!0.865 50.02145022 #VALUE!0.866 50.02572612 #VALUE!0.867 50.030024 #VALUE!0.868 50.03434418 #VALUE!0.869 50.038687 #VALUE!

0.87 50.04305278 #VALUE!0.871 50.04744187 #VALUE!0.872 50.05185462 #VALUE!0.873 50.05629139 #VALUE!0.874 50.06075253 #VALUE!0.875 50.06523843 #VALUE!0.876 50.06974947 #VALUE!0.877 50.07428605 #VALUE!0.878 50.07884855 #VALUE!0.879 50.08343739 #VALUE!

0.88 50.088053 #VALUE!0.881 50.09269579 #VALUE!0.882 50.09736622 #VALUE!0.883 50.10206473 #VALUE!0.884 50.10679178 #VALUE!0.885 50.11154786 #VALUE!0.886 50.11633344 #VALUE!0.887 50.12114901 #VALUE!0.888 50.12599511 #VALUE!

0.889 50.13087223 #VALUE!0.89 50.13578093 #VALUE!

0.891 50.14072176 #VALUE!0.892 50.14569527 #VALUE!0.893 50.15070206 #VALUE!0.894 50.15574271 #VALUE!0.895 50.16081784 #VALUE!0.896 50.16592808 #VALUE!0.897 50.17107408 #VALUE!0.898 50.1762565 #VALUE!0.899 50.18147602 #VALUE!

0.9 50.18673336 #VALUE!0.901 50.19202922 #VALUE!0.902 50.19736437 #VALUE!0.903 50.20273955 #VALUE!0.904 50.20815557 #VALUE!0.905 50.21361324 #VALUE!0.906 50.21911339 #VALUE!0.907 50.22465689 #VALUE!0.908 50.23024463 #VALUE!0.909 50.23587753 #VALUE!

0.91 50.24155654 #VALUE!0.911 50.24728262 #VALUE!0.912 50.2530568 #VALUE!0.913 50.25888012 #VALUE!0.914 50.26475365 #VALUE!0.915 50.27067851 #VALUE!0.916 50.27665585 #VALUE!0.917 50.28268686 #VALUE!0.918 50.28877278 #VALUE!0.919 50.29491487 #VALUE!

0.92 50.30111447 #VALUE!0.921 50.30737295 #VALUE!0.922 50.31369172 #VALUE!0.923 50.32007225 #VALUE!0.924 50.32651608 #VALUE!0.925 50.3330248 #VALUE!0.926 50.33960004 #VALUE!0.927 50.34624353 #VALUE!0.928 50.35295704 #VALUE!0.929 50.35974243 #VALUE!

0.93 50.36660162 #VALUE!0.931 50.37353662 #VALUE!0.932 50.38054953 #VALUE!0.933 50.38764252 #VALUE!0.934 50.39481788 #VALUE!0.935 50.40207797 #VALUE!0.936 50.40942528 #VALUE!0.937 50.41686241 #VALUE!0.938 50.42439208 #VALUE!0.939 50.43201711 #VALUE!

0.94 50.4397405 #VALUE!0.941 50.44756535 #VALUE!0.942 50.45549496 #VALUE!

0.943 50.46353275 #VALUE!0.944 50.47168235 #VALUE!0.945 50.47994756 #VALUE!0.946 50.48833238 #VALUE!0.947 50.49684103 #VALUE!0.948 50.50547796 #VALUE!0.949 50.51424789 #VALUE!

0.95 50.52315577 #VALUE!0.951 50.53220688 #VALUE!0.952 50.54140678 #VALUE!0.953 50.55076139 #VALUE!0.954 50.56027699 #VALUE!0.955 50.56996025 #VALUE!0.956 50.57981829 #VALUE!0.957 50.5898587 #VALUE!0.958 50.60008957 #VALUE!0.959 50.61051958 #VALUE!

0.96 50.62115799 #VALUE!0.961 50.63201477 #VALUE!0.962 50.64310064 #VALUE!0.963 50.65442713 #VALUE!0.964 50.66600668 #VALUE!0.965 50.67785276 #VALUE!0.966 50.68997997 #VALUE!0.967 50.70240414 #VALUE!0.968 50.71514255 #VALUE!0.969 50.72821404 #VALUE!

0.97 50.74163925 #VALUE!0.971 50.75544084 #VALUE!0.972 50.76964377 #VALUE!0.973 50.78427564 #VALUE!0.974 50.79936703 #VALUE!0.975 50.81495205 #VALUE!0.976 50.83106879 #VALUE!0.977 50.84776006 #VALUE!0.978 50.86507419 #VALUE!0.979 50.88306601 #VALUE!

0.98 50.90179811 #VALUE!0.981 50.92134237 #VALUE!0.982 50.94178197 #VALUE!0.983 50.96321386 #VALUE!0.984 50.98575202 #VALUE!0.985 51.00953181 #VALUE!0.986 51.03471566 #VALUE!0.987 51.06150095 #VALUE!0.988 51.09013093 #VALUE!0.989 51.12091034 #VALUE!

0.99 51.15422828 #VALUE!0.991 51.19059304 #VALUE!0.992 51.23068701 #VALUE!0.993 51.27545774 #VALUE!0.994 51.3262782 #VALUE!0.995 51.38525131 #VALUE!0.996 51.45585101 #VALUE!

0.997 51.54448117 #VALUE!0.998 51.66521507 #VALUE!0.999 51.86159516 #VALUE!

VALUE AT RISK CALCULATION FOR PORTFOLIO OF OPTIONS DEPENDENT ON A SINGLE STOCKUses Results in Chapter 20 of Options, Futures and Other Derivatives, 7e

Problem 20.21 in Options, Futures and Other Derivatives, 7e is based on this application

Type Number0 10001 100 55 0.5 11 500 50 0.25 11 1600 50 0.2 0

z_q -2.3263w_q #VALUE!

We calculate the analytic VaR by generating 1000 equally likely portfolio values

45 46 47 48 49 50 51 52 530

2

4

6

8

10

12

Asset Price

Po

rtfo

lio

Val

ue

CALCULATION OF A STATIC OPTIONS REPLICATION POSITIONCarries out calculations for the example in Section 24.14 of Options, Futures and Other Derivatives, 7e

Problem 24.27 in Options, Futures, and Other Derivatives, 7e is based on this application

Barrier OptionStock 50 IsUp 1Strike 50 IsIn 0Barrier 60 IsCall 1

r 10.00%q 0%

vol 30%t 0.75 Barrier Price #VALUE!

A four option hedge Hedge Portfolio

Type Number K Tmat IsCall1 1 50 0.75 1

0.5 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.75 10.25 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.5 1

0 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.25 10 50 Hedge Price

A sixteen option hedge Hedge Portfolio

Type Number K Tmat IsCall1 1 50 0.75 1

0.7 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.75 10.65 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.7 10.6 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.65 1

0.55 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.6 10.5 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.55 1

0.45 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.5 10.4 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.45 1

0.35 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.4 10.3 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.35 1

0.25 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.3 10.2 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.25 1

0.15 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.2 10.1 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.15 1

0.05 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.1 10 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.05 10 50 Hedge Price

Hedge Time

S at which value is

zero

Portfolio without

this Opt.Value of this Opt.

Number needed to

Hedge

Hedge Time

S at which value is

zero

Portfolio without

this Opt.Value of this Opt.

Number needed to

Hedge

CALCULATION OF A STATIC OPTIONS REPLICATION POSITIONCarries out calculations for the example in Section 24.14 of Options, Futures and Other Derivatives, 7e

Problem 24.27 in Options, Futures, and Other Derivatives, 7e is based on this application

Return 0 = Price0 1 = Delta

2 = Gamma3 = Vega

#VALUE!#VALUE!#VALUE!#VALUE!

A better sixteen option hedge Hedge Portfolio

Type Number K Tmat IsCall1 1 50 0.750 1

#VALUE! 0.745 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.750 1#VALUE! 0.74 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.745 1#VALUE! 0.73 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.740 1#VALUE! 0.72 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.730 1#VALUE! 0.71 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.720 1#VALUE! 0.7 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.710 1#VALUE! 0.68 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.700 1#VALUE! 0.65 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.680 1#VALUE! 0.6 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.650 1#VALUE! 0.55 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.600 1#VALUE! 0.5 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.550 1#VALUE! 0.4 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.500 1#VALUE! 0.3 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.400 1#VALUE! 0.2 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.300 1#VALUE! 0 60 #VALUE! #VALUE! #VALUE! 1 ### 60 0.200 1#VALUE! 0 50 Hedge Price

Portfolio Value with this Opt.

Portfolio Value with this Opt.

Hedge Time

S at which value is

zero

Portfolio without

this Opt.Value of this Opt.

Number needed to

Hedge

#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!

Portfolio Value with this Opt.

TESTS CONVERGENCE OF TRINOMIAL TREE FOR A EUROPEAN BOND OPTIONThis carries out calculations for Example 30.1 in Options, Futures, and Other Derivatives, 7e

Problem 30.26 in Options, Futures, and Other Derivatives, 7e is based on this application

Term Structure0.008219 5.018% Time to Ex. 10.084932 4.983% BondLife 90.169863 4.972% Coupon 0.00%0.257534 4.962% Principal 1000.506849 4.991% Payment Freq 21.005479 5.094%2.00274 5.797% IsCall 13.00274 6.306% Result 04.00274 6.735%5.00274 6.948% Sigma 1.00%

6.010959 7.088% RevRate 10.00%7.008219 7.275% Strike 558.005479 7.309% IsQuotedStrike 09.005479 7.398%10.00822 7.490%

nSteps Tree Analytic5 #VALUE! #VALUE!6 #VALUE! #VALUE!7 #VALUE! #VALUE!8 #VALUE! #VALUE!9 #VALUE! #VALUE!

10 #VALUE! #VALUE!11 #VALUE! #VALUE!12 #VALUE! #VALUE!13 #VALUE! #VALUE!14 #VALUE! #VALUE!15 #VALUE! #VALUE!16 #VALUE! #VALUE!17 #VALUE! #VALUE!18 #VALUE! #VALUE!19 #VALUE! #VALUE!20 #VALUE! #VALUE!21 #VALUE! #VALUE!22 #VALUE! #VALUE!23 #VALUE! #VALUE!24 #VALUE! #VALUE!25 #VALUE! #VALUE!26 #VALUE! #VALUE!27 #VALUE! #VALUE!28 #VALUE! #VALUE!29 #VALUE! #VALUE!30 #VALUE! #VALUE!31 #VALUE! #VALUE!32 #VALUE! #VALUE!33 #VALUE! #VALUE!34 #VALUE! #VALUE!

0 10 20 30 40 50 60 70 800.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

Trinomial Convergence

Tree

Analytic

nSteps

35 #VALUE! #VALUE!36 #VALUE! #VALUE!37 #VALUE! #VALUE!38 #VALUE! #VALUE!39 #VALUE! #VALUE!40 #VALUE! #VALUE!41 #VALUE! #VALUE!42 #VALUE! #VALUE!43 #VALUE! #VALUE!44 #VALUE! #VALUE!45 #VALUE! #VALUE!46 #VALUE! #VALUE!47 #VALUE! #VALUE!48 #VALUE! #VALUE!49 #VALUE! #VALUE!50 #VALUE! #VALUE!51 #VALUE! #VALUE!52 #VALUE! #VALUE!53 #VALUE! #VALUE!54 #VALUE! #VALUE!55 #VALUE! #VALUE!56 #VALUE! #VALUE!57 #VALUE! #VALUE!58 #VALUE! #VALUE!59 #VALUE! #VALUE!60 #VALUE! #VALUE!61 #VALUE! #VALUE!62 #VALUE! #VALUE!63 #VALUE! #VALUE!64 #VALUE! #VALUE!65 #VALUE! #VALUE!66 #VALUE! #VALUE!67 #VALUE! #VALUE!68 #VALUE! #VALUE!69 #VALUE! #VALUE!70 #VALUE! #VALUE!71 #VALUE! #VALUE!72 #VALUE! #VALUE!73 #VALUE! #VALUE!74 #VALUE! #VALUE!75 #VALUE! #VALUE!76 #VALUE! #VALUE!77 #VALUE! #VALUE!78 #VALUE! #VALUE!79 #VALUE! #VALUE!80 #VALUE! #VALUE!

TESTS CONVERGENCE OF TRINOMIAL TREE FOR A EUROPEAN BOND OPTIONThis carries out calculations for Example 30.1 in Options, Futures, and Other Derivatives, 7e

Problem 30.26 in Options, Futures, and Other Derivatives, 7e is based on this application

0 10 20 30 40 50 60 70 800.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

Trinomial Convergence

Tree

Analytic

nSteps