Question

Suppose today's stock price of McDonald’s is $150. With probability, 60% the price will rise to $175 in one year and with probability, 40% it will fall to $140 in one year. What is the current price of a European call option with one year until maturity with a strike price of $160 if the risk-free rate of interest is 4%? Use a binomial tree.

Answer 1

Binomial Pricing of a call option = > C= [{Cu *p + Cd * (1-p)}/ Risk free rate]

P = (1+Risk Free Rate) – (1-Down %) / (1+Up %) – (1-Down %)

Risk Free Rate = 0.04

Down % = 40%

Up % = 60%

Probability = (1.04) – (1-0.40)/ (1+0.60) – (1-0.40) = 0.44/ 1 = 0.44

Probability of decrease = 1-0.44= 0.56

Cu = {Strike Price * (1+ rise Price) – Strike Price} = $160*1.60- $160 = $96

Cd = 0 (if the price is lower than the exercise price then the call will not be exercised)

Or, Price of one-year call = $96*0.44/ (1.04) = $40.62

Hence under the binomial model price of one-year call option would be $40.62