Question

A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 8% with a probability of 50% or down by 4% with a probability of 50%. The risk-free interest rate is 4% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $50? Use binomial tree method to solve this problem.

Answer 1

Answer- Shown the two period binomial tree in the image attached, rest solution is typed here only

Current market price on expiry	Exercise price	Option premium on expiry (CMP-EP)	Probability	Expected Opyion premium on expiry
58.32	50	8.32	0.50*0.50	2.08
51.84	50	1.84	0.50*0.50	0.46
51.84	50	1.84	0.50*0.50	0.46
46.08	50	0	0.50*0.50	0
Total				3

Value of six month call option= 3*e^-0.04*6/12

Solving above as e=2.71828, we get value of call option = 2.94