Question

You observe a 50 stock price for a non-dividend paying stock. The call has two years to mature, the periodically compounded risk-free interest rate is 5%, the exercise price is 50, u = 1.356, d = 0.744. Assume the call option is European-style.

The current value of the call option is closest to:

a) 9.53

b) 9.71

c) 9.87

Answer 1

a) 9.53

Probability of up-move =

Probability of up-move = (e^(0.05*2)-0.744)/(1.356-0.744) = 0.59014

Probability of down-move = 1- = 0.40985

Price of the stock when stock up-moves = 50*1.356 = 67.8

Price of the stock when stock up-moves = 50*0.744 = 37.2

The stock only has a positive pay-off when the stock price up-moves

When the stock down-moves, the call option payoff is 0 since Spot price at maturity is lesser than strike price at maturity

Call option price = Expected payoff at maturity*Present value factor

Call option price =0.59014*(67.8-50)*(1/(1.05*1.05) =9.527

Hence, call option price = 9.53