Question

You are attempting to value a call option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $88. The risk-free rate of interest is 12%.

Calculate the call option’s value using the two-state stock price model. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

The value of the call option today is $9.38

Step-by-step explanation:

The two-state stock pricing model or the expectations model bases price or value of option on the assumption that there is no arbitrage profit opportunity and the value of the call option is the present value of the expected future winning for the long call.

The call option will have a value of (130 - 109 = 21) if the prices go up or a value of (88 - 109 = -21) if the prices go down. The call option will only be exercised if the market value is more than the exercise price. Thus, the expected value of winning after one year if is,

Value after one year = 21 * 0.5 + 0 * 0.5

Value after one year = $10.5

The value of 0 is taken because the call will not be exercised if the prices go down.

Today, the long call is expected to earn $10.5 one year from now. The present value of this amount today is the price of the call option assuming no arbitrage profit opportunity.

PV = 10.5 / 1.12 = $9.375 rounded off to $9.38

The value of the call option today is $9.38