You are attempting to value a call option with an exercise price of $105 and one year to expiration. The underlying stock pays no dividends, its current price is $105, and you believe it has a 50% chance of increasing to $122 and a 50% chance of decreasing to $88. The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model.

The value of the call option today is $7.73

Explanation:

The value or price of the call option under the two state model is calculated based on the assumption that there is no opportunity for arbitrage profit. The value of call option will be based on the return in case the call option is exercised and the probability of earning that return.

The strike price is $105

The return if price goes to $122 and option is exercised is 122 - 105 = $17

The return if the price goes down to $88 will be 0 as the call option will not be exercised.

Thus, the expected return is = 0.5 * 17 + 0.5 * 0  =  $8.5

This return will be earned after 1 year. To calculate the value of the call option today, we need to discount this return to present value using the risk free rate.

V0 or value today = 8.5 / (1+0.1)  =  $7.727 rounded off to $7.73