Question

Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $64.00 currently and pays an annual dividend of $1.17. The standard deviation of the stock’s returns is 0.09 and risk-free interest rate is 2.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.)

Put value            $

Answer 1

In this case, S0 = 64; X = 62; r = 0.025; sd = 0.09 and T = 4/12

d1 = [{ln(S0/X)} + {t(r - q + sd²/2)}] / [sd(t)^1/2]

= [{ln(64/62)} + {(4/12)(0.025 + 0.09²/2)}] / [0.09(4/12)^1/2]

= 0.0414 / 0.0520 = 0.797359821

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

= 0.7974 - [0.09(4/12)^1/2]

= 0.7974 - 0.0520 = 0.7454

P = [X * e^-rt * N(-d2)] - [S0 * e^-qt * N(-d1)]

= [$62 * e^{-0.025*(4/12)} * N(-0.7454)] - [$64 * e^-0*(4/12) * N(-0.7974)]

= [$62 * 0.9917 * 0.2280] - [$64 * 0.2126]

= $14.02 - $13.61 = $0.4096