fm3_problems19 - Exercise 1 Black-Scholes option pricing...

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Exercise 1 Page 1 Black-Scholes option pricing formula S 50 current stock price X 50 exercise price r 10.00% risk-free rate of interest T 0.5 time to maturity of option (in years) Sigma 25% stock volatility 0.3712 #MACRO? 0.1945 #MACRO? 0.6448 #MACRO? 0.5771 #MACRO? call price 4.79 #MACRO? put price 2.35 #MACRO? d 1 d 2 N(d 1 ) N(d 2 )
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Exercise 2 Page 2 Black-Scholes option pricing formula S 50 current stock price X 50 exercise price r 10.00% risk-free rate of interest T 0.5 time to maturity of option (in years) Sigma 25% stock volatility 0.3712 <--(LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.1945 0.6448 0.5771 call price 4.79 put price 2.35 <-- call price - S + X*Exp(-r*T): by Put-Call parity 2.35 Below: Data tables for the sensitivities Sensitivity of Call Price to Initial Stock Price 4.79 36 0.18 38 0.36 40 0.67 42 1.12 44 1.75 46 2.57 48 3.59 50 4.79 52 6.16 54 7.68 56 9.31 58 11.05 60 12.85 62 14.72 64 16.63 Sensitivity of Put Price to Sigma 2.35 10.0% 0.49 12.5% 0.77 15.0% 1.07 17.5% 1.38 20.0% 1.7 22.5% 2.02 25.0% 2.35 27.5% 2.68 30.0% 3.01 32.5% 3.35 35.0% 3.68 37.5% 4.02 d 1 d 2 <-- d 1 - sigma*SQRT(T) N(d 1 ) <--- Uses formula NormSDist(d 1 ) N(d 2 ) <--- Uses formula NormSDist(d 2 ) <-- S*N(d 1 )-X*exp(-r*T)*N(d 2 ) <-- X*exp(-r*T)*N(-d 2 )-S*N(d 1 ): direct formula 34 39 44 49 54 59 64 0 1 2 3 4 5 6 Sensitvity of Call Price to Stock Price Stock Price Call Price 0.5 1 1.5 2 2.5 Sensitivty of Put Price to Sigma Put Price
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Exercise 2 Page 3 40.0% 4.35 Sensitivity of Call Price to time to Maturity 4.79 0.2 2.74 0.3 3.49 0.4 4.17 0.5 4.79 0.6 5.38 0.7 5.94 0.8 6.47 0.9 6.99 1 7.49 1.1 7.97 1.2 8.45 1.3 8.91 1.4 9.36 Sensitivity of Call Price to Interest Rate 4.79 5% 4.13 6% 4.26 7% 4.39 8% 4.52 9% 4.65 10% 4.79 11% 4.93 12% 5.07 13% 5.21 14% 5.36 15% 5.5 16% 5.65 17% 5.8 18% 5.95 Sensitivity of Put Price to exercise Price 2.35 38 0.1 40 0.2 42 0.38 44 0.66 46 1.07 48 1.63 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% 45.0% 0 Sigma 0.4 0.6 0.8 1 1.2 1.4 1.6 0 1 2 3 4 5 6 Sensitivity of Call Price to Time to Maturity Time to Maturity Call Price 5% 7% 9% 11% 13% 15% 17% 19% 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 Sensitivity of Call Price to Interest Rate Interest Rate (r) 1.5 2 2.5 Sensitvity of Put Price to Exercise Price
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Exercise 2 Page 4 50 2.35 52 3.24 54 4.29 56 5.5 58 6.85 60 8.31 62 9.88 64 11.53 38 43 48 53 58 63 68 0 0.5 1 1.5 Exercise Price (X) Put Price
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Exercise 2 Page 5
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Exercise 2 Page 6
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Exercise 2 Page 7
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Exercise 3 Page 8 Black-Scholes option pricing formula S 50 current stock price X 50 exercise price r 10.00% risk-free rate of interest T 0.5 time to maturity of option (in years) Sigma 25% stock volatility 0.3712 <--(LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) 0.1945 0.6448 0.5771 call price 4.79 put price 2.35 <-- call price - S + X*Exp(-r*T): by Put-Call parity 2.35 Stock B-S Intrinsic Price Value Value 4.79 36 0.1796 0 38 0.3639 0 40 0.6663 0 42 1.1198 0 44 1.7503 0 46 2.5725 0 48 3.5891 0 50 4.7911 0 52 6.1612 2 54 7.6768 4 56 9.3132 6 58
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This note was uploaded on 01/23/2011 for the course FGB 780 taught by Professor Edwardchang during the Spring '09 term at Missouri State University-Springfield.

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fm3_problems19 - Exercise 1 Black-Scholes option pricing...

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