Question

You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $124 and a 50% chance of decreasing to $76. The risk-free rate of interest is 8%. Calculate the call option's value using the two-state stock price model.

Answer 1

High price=Current price*up move=100*1.2667=126.67

Low price=Current price*down move=100*0.8933=89.33

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.08*1)-0.8933)/(1.2667-0.8933)=0.5

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(124-100,0)

=Max(24,0)

=24

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(76-100,0)

=Max(-24,0)

=0

Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.08*1)*(0.5*24+(1-0.5)*0)

=11.08