Question

The stock price is currently $50. The stock price annual up-move factor is 1.15. The risk-free rate is 3.9%. What is the value of a 1-year European call option with an exercise price of $52.

		$ 3.21
		$ 2.38
		$ 2.73
		$ 1.95

Answer 1

Using binomial tree:

Step1: Down move factor = 1 / up move factor = 1/1.15

Step2: We will calculate up move probablity and down move probablity.

Up move probablity = (e ^(rf *t) - down move factor) / (up move factor - down move factor)

Up move probablity = {e^(0.039) - (1/1.15)}/ (1.15 - 1/1.15) =0.607

Down move probablity = 0.393

Step3: We will calculate payoff of call option and then expected value of payoff will be calculated using probablity of upmove and downmove.

The expected value comes out to 3.3385.

Step4: Value of call option = Present value of expected value of payoff discounted @3.9%.

Value of call option = $3.21 Answer

Option A is correct.