Question

The price of Chive Corp. Stock will be either $67 or $91 at the end of the year. Call option are available with one year to expiration-bills currently yield 4 percent. b) Suppose the current price of the company stock is a $75. what is the value of the call option if the exercise price is $82 per share?

Answer 1

u = S_u / S₀ = 91 / 75 = 1.2133 ; d = S_d / S₀ = 67 / 75 =  0.8933

Risk neutral probability of up move, p = (e^rt - d) / (u - d) where r = risk free rate = 4% and t = 1 year

Hence, p = (e^{0.04 x 1} - 0.8933) / (1.2133 - 0.8933) =  0.4609

C_u = max (S_u - K, 0) = max (91 - 82, 0) = 9

C_d = max (S_d - K, 0) = max (67 - 82, 0) = 0

Hence, value of the call option today = [p x C_u + (1 - p) x C_d] x e^-rt = [0.4609 x 9 + (1 - 0.4609) x 0] x e^{-0.04 x1} = $  3.9852