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.)
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
A stock is currently priced at $68 and has an annual standard deviation of 48 percent....
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