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

Stock Price	150
Strike Price	160
Stock Price after one year with 60% probability	175
Stock Price after one year with 40% probability	140
Risk Free Rate	4%
Value of the european call at the expiration	max( 0, (Stock Price-Strike Price))
Value of the Call, when stock reaches to 175	max(0, (175-160)	15
Value of the Call, when stock reaches to 140	max(0, (140-160)	0
These values of the call is at the end of year one with different different probability.
To compute the call price today, we need to calculate the present value of the call options at both end and calcualted the expected value on the basis of probability
Call price with 60% probability at t=0 with discounted factor	15/1.04	14.42
Call price with 40% probability at t=0 with discounted factor	0/1.04	0.00
At t=0 estimated call price will be the weighted average number of both the end	60%*14.42+40%*0	8.65