Question

You are attempting to value a call option with an exercise price of $55 and one year to expiration. The underlying stock pays no dividends, its current price is $55, and you believe it has a 50% chance of increasing to $85 and a 50% chance of decreasing to $25. The risk-free rate of interest is 6%. Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.)  

Value of the call            $   

A put option on a stock with a current price of $41 has an exercise price of $43. The price of the corresponding call option is $3.45. According to put-call parity, if the effective annual risk-free rate of interest is 5% and there are three months until expiration, what should be the value of the put? (Do not round intermediate calculations. Round your answer to 2 decimal places.)  

Value of the put            $

Answer 1

S = X = 55

Su = 85, Cu = 30

Sd = 25, Cd = 0

C = [p*Cu + (1 - p)*Cd]/R

As given probability is not the risk-neutral probability, we should use portfolio method.

H = (30 - 0)/(85 - 25) = 30/60 = 0.5

B = (Cu - SuH)/R = (30 - 85*0.5)/1.06 = -11.79

C = S*H + B = 55*0.5 - 11.79 = 15.71

Value of call = $15.71

S = 41, X = 43, C = 3.45, r = 5%, T = 3/12

Using put-call parity equation

P + S = C + PV(X)

P = C + PV(X) - S = 3.45 + 43*1.05^(-3/12) - 41 = 4.93

Value of put = $4.93