Question

Suppose IBM's stock price is currently $100. In the next year it will either fall to $70 or rise to $130. What is the price today of a one-year European call option on IBM with an exercise price of 100? The one-year risk-free interest rate is 2% per year. 6 10 0 15.69

Answer 1

Upmove (U)= High price/current price=130/100=1.3

Down move (D)= Low price/current price=70/100=0.7

Risk neutral probability for up move

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

=(e^(0.02*1)-0.7)/(1.3-0.7)=0.53367

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(130-100,0)

=Max(30,0)

=30

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(70-100,0)

=Max(-30,0)

=0

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

=e^(-0.02*1)*(0.533669*30+(1-0.533669)*0)

=15.69