Question

A stock is currently priced at $68 and has an annual standard deviation of 48 percent. The dividend yield of the stock is 3.5 percent, and the risk-free rate is 6.5 percent. What is the value of a call option on the stock with a strike price of $65 and 55 days to expiration? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Answer 1

d1 = [{ln(S0/X)} + {t(r - q + ²/2)}] / [(t)^1/2]

= [{ln(68/65)} + {(55/365)(0.065 - 0.035 + 0.48²/2)}] / [0.48(55/365)^1/2]

= 0.0670 / 0.1863 = 0.3596

d2 = d1 - [(t)^1/2]

= 0.3596 - [0.48(55/365)^1/2]

= 0.3596 - 0.1863 = 0.1733

C = [S0 x e^-qt x N(d1)] - [X x e^-rt x N(d2)]

= [68 x e^{-0.035*(55/365)} x N(0.3596)] - [65 x e^{-0.065*(55/365)} x N(0.1733)]

= [68 x e^-0.0053 x 0.6404] - [65 x e^-0.0098 x 0.5688]

= 43.32 - 36.61 = 6.71, or $6.71