Final answer:
To value a call option using the two-state stock price model, calculate the expected payoff for each possible outcome, weight them by the probabilities, and discount them back to the present using the risk-free rate of interest. Therefore, the value of the call option is $8.48.
Step-by-step explanation:
To calculate the call option's value using the two-state stock price model, we need to calculate the expected payoff for each possible stock price outcome and then discount them back to the present using the risk-free rate of interest. In this case, the stock has a 50% chance of increasing to $121 and a 50% chance of decreasing to $83, with an exercise price of $102.
For the stock price of $121, the option payoff is $121 - $102 = $19. For the stock price of $83, the option payoff is $0. Since the stock pays no dividends, the expected payoff is the weighted average of the two possible payoffs, using the probabilities.
Calculation: ($19 * 0.5) + ($0 * 0.5) = $9.50
Next, we discount the expected payoff back to the present using the risk-free rate of interest. In this case, the interest rate is 12%. So, the present value of the call option is:
Present Value = Expected Payoff / (1 + Interest Rate)
Calculation: $9.50 / (1 + 0.12) = $8.48
Therefore, the value of the call option is $8.48.