Question

A stock currently trades at $40. The continuously compounded risk-free rate of interest is 7%, and the volatility of the stock return is 35%. Use the Black-Scholes formula to compute each of the following (round each answer to the nearest penny). a) The price of a 0.25-year European call option, struck at $45. Price = $ . ------------------- b) The price of a 0.25-year European put option, struck at $45. Price = $ .----------------------

Answer 1

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

= [{ln(40/45)} + {0.25(0.07 + 0.35²/2)}] / [0.35(0.25)^1/2]

     = -0.0850 / 0.1750 = -0.4855

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

     = -0.4855 - [0.35(0.25)1/2]

= -0.4855 - 0.1750 = -0.6605

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

         = [40 x e^-0*0.25 x N(-0.4855)] - [45 x e^-0.07*0.25 x N(-0.6605)]

         = [40 x 0.3137] - [45e^-0.07*0.25 x 0.2545]

         = 12.55 - 11.25 = $1.29

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

= [45 x e^-0.07*0.25 x N(0.6605)] - [40 x e^-0*0.25 x N(0.4855)]

         = [45e^-0.07*0.25 x 0.7455] - [40 x 0.6863]

         = 32.97 - 27.45 = $5.51