Question

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            $ ?

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