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 |

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d2 =
#N/A
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