Question

Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $45, (2) exercise price is $50, (3) time to expiration is 3 months, (4) annualized risk-free rate is 3%, and (5) variance of stock return is 0.50.

AND based on the information above, find the value of a put with a $50 exercise price. (SHOW CALCULATIONS PLEASE)

Answer 1

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

    = [{ln(45/50)} + {0.25(0.03 + 0.50/2)}] / [0.50^0.5(0.25)^1/2]

    = -0.0354 / 0.3536 = -0.1000

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

     = -0.1000 - [0.50^0.5(0.25)^1/2]

= -0.1000 - 0.3536 = -0.4536

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

         = [45 x e^-0*0.25 x N(-0.1000)] - [50 x e^-0.03*0.25 x N(-0.4536)]

         = [45 x 0.4602] - [50e^-0.03*0.25 x 0.3251]

         = 20.71 - 16.13 = 4.58, or $4.58

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

         = [50 x e^-0.03*0.25 x N(0.4536)] - [45 x e^-0*0.25 x N(0.1000]

         = [50e^-0.10*0.25 x 0.6749] - [45 x 0.5398]

         = 33.49 - 24.29 = 9.20, or $9.20