Question

# Use the Black-Scholes model to calculate the theoretical value of a DBA December 45 call option....

Use the Black-Scholes model to calculate the theoretical value of a DBA December 45 call option. Assume that the risk free rate of return is 6 percent, the stock has a variance of 36 percent, there are 91 days until expiration of the contract, and DBA stock is currently selling at \$50 in the market. [Hint: Use Excel's NORMSDIST() function to find N(d1) and N(d2)]

Std dev = variance^(1/2)= 0.36^(1/2) = 60%

 As per Black Scholes Model Value of call option = S*N(d1)-N(d2)*K*e^(-r*t) Where S = Current price = 50 t = time to expiry = 0.249315 K = Strike price = 45 r = Risk free rate = 6.0% q = Dividend Yield = 0.00% σ = Std dev = 60% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(50/45)+(0.06-0+0.6^2/2)*0.249315)/(0.6*0.249315^(1/2)) d1 = 0.55141 d2 = d1-σ*t^(1/2) d2 =0.55141-0.6*0.249315^(1/2) d2 = 0.251821 N(d1) = Cumulative standard normal dist. of d1 N(d1) =0.709324 N(d2) = Cumulative standard normal dist. of d2 N(d2) =0.59941 Value of call= 50*0.709324-0.59941*45*e^(-0.06*0.249315) Value of call= 8.89

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