Question

# . Use the Black-Scholes model to find the price for a call option with the following...

. Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is \$45, (2) exercise price is \$50, (3) time to expiration is 3 months, (4) annualized risk-free rate is 3%, and (5) variance of stock return is 0.50.

. Using the information from question above, find the value of a put with a \$50 exercise price.

Std dev = variance^(1/2)=0.5^(1/5)=87.06%

 As per Black Scholes Model Value of call option = S*N(d1)-N(d2)*K*e^(-r*t) Where S = Current price = 45 t = time to expiry = 0.25 K = Strike price = 50 r = Risk free rate = 3.0% q = Dividend Yield = 0% σ = Std dev = 87% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(45/50)+(0.03-0+0.8706^2/2)*0.25)/(0.8706*0.25^(1/2)) d1 = -0.007162 d2 = d1-σ*t^(1/2) d2 =-0.007162-0.8706*0.25^(1/2) d2 = -0.442462 N(d1) = Cumulative standard normal dist. of d1 N(d1) =0.497143 N(d2) = Cumulative standard normal dist. of d2 N(d2) =0.329077 Value of call= 45*0.497143-0.329077*50*e^(-0.03*0.25) Value of call= 6.04
 As per put call parity Call price + PV of exercise price = Spot price + Put price 6.04+50/(1+0.03)^0.25=45+Put value Put value = 10.67