Question

You are attempting to value a call option with an exercise price of $150 and one year to expiration. The underlying stock pays no dividends. Its current price is $100. The stock price either increases by a factor of 1.5, or decreases by a factor of 0.5, every six months. The risk-free rate of interest is 2% per year (or 1% per six-month period).

What is the value of this call option using the two-period binomial option pricing model? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Value of the call  

Answer 1

Strike price = $150

Stock price = $100

Stock price in next period can be either 1.5*100 = 150 or 0.5*100 = 50

In second period for upper node, it can be 150*1.5 = 225 or 150*0.5 =75

In second period for lower node, it can be 50*1.5 = 75 or 50*0.5 =25

So in second period, stock price can be 225, 75 or 25

Since strike price = 150

Payoff in case of 225 = max(225-150,0) = 75

Payoff in case of 75 = max(75-150,0) = 0

Payoff in case of 25= max(25-150,0) = 0

Net Payoff of call option = 0.5*0.5*75 + 0.5*0.5*0+ 0.5*0.5*0+ 0.5*0.5*0 = 18.75

Call option premium = 18.75/(1+2%/2)^2 = $ 18.381