You own a one-year call option to buy one acre of Los Angeles real estate. The exercise price is $2.19 million, and the current, appraised market value of the land is $1.89 million. The land is currently used as a parking lot, generating just enough money to cover real estate taxes. The annual standard deviation is 16% and the interest rate 10%. How much is your call worth? Use the Black–Scholes formula
(Answer in $000s with one decimal place.)
As per Black Scholes Model | ||||||
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t) | ||||||
Where | ||||||
S = Current price = | 1890000 | |||||
t = time to expiry = | 1 | |||||
K = Strike price = | 2190000 | |||||
r = Risk free rate = | 10.0% | |||||
q = Dividend Yield = | 0% | |||||
σ = Std dev = | 16% | |||||
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | ||||||
d1 = (ln(1890000/2190000)+(0.1-0+0.16^2/2)*1)/(0.16*1^(1/2)) | ||||||
d1 = -0.215779 | ||||||
d2 = d1-σ*t^(1/2) | ||||||
d2 =-0.215779-0.16*1^(1/2) | ||||||
d2 = -0.375779 | ||||||
N(d1) = Cumulative standard normal dist. of d1 | ||||||
N(d1) =0.41458 | ||||||
N(d2) = Cumulative standard normal dist. of d2 | ||||||
N(d2) =0.353541 | ||||||
Value of call= 1890000*0.41458-0.353541*2190000*e^(-0.1*1) | ||||||
Value of call= 82981.49 = 83 (000s) |
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