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 $142 and a 50% chance of decreasing to $76. The risk-free rate of interest is 12%. Calculate the call option's value using the two-state stock price model.

The two-state stock pricing model is one that prices are based on the assumption that there is no arbitrage profit opportunity as well as the fact that the call option's value will be the present value(PV) of the expected future winnings for long call.

Now, value of the call option if the prices go up will be;

142 - 109 = $32

While if the prices go down, it will be;

76 - 109 = -$33

The call option in this case can only be utilized when the market value exceeds the exercise price.

Therefore, the expected winnings value after one year will be;

Value after one year = (32 × 0.5) + (0 × 0.5)

Value after one year = $16

We used 0 in the multiplication because the call wouldn't be utilized for when the prices go down.

one year from now the long call can be expected to earn $16 .

Thus, today the present value of this amount will be the price of the call option if we take into cognizance that here will be no arbitrage profit opportunity.

With risk-free rate of interest is 12%, we have;

PV = 16/1.12 = $14.29