Question

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)]

Answer 1

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