Question

# Use the Black-Scholes model to find the value for a European put option that has an...

Use the Black-Scholes model to find the value for a European put option that has an exercise price of \$49.00 and 0.4167 years to expiration. The underlying stock is selling for \$40.00 currently and pays an annual dividend yield of 0.01. The standard deviation of the stock’s returns is 0.4400 and risk-free interest rate is 0.06. (Round your final answer to 2 decimal places. Do not round intermediate calculations.)

Put value            \$ ?

#### Homework Answers

Answer #1

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

= [{ln(40/49)} + {0.4167(0.06 - 0.01 + 0.442/2)}] / [0.44(0.4167)1/2]

= -0.1418 / 0.2840 = -0.4991

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

= -0.4991 - [0.44(0.4167)1/2]
= -0.4991 - 0.2840 = -0.7832

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

= [49 x e-0.06*0.4167x N(0.7832)] - [40 x e-0.01*0.4167 x N(0.4991)]

= [49e-0.06*0.4167 x 0.7832] - [40 x 0.6912]

= 37.43 - 27.65 = 9.78, or \$9.78

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