Question

you are attempting to value a put option with an exercise price of $107 and one year to expiration. the underlying stock pays no dividends, its current price is $107, and you believe it has a 50% chance of increasing to $123 and a 50% chance of decreasing to $91. the risk-free rate of interest is 12%. calculate the value of a put option with exercise price $107.

Answer 1

To calculate the value of a put option with an exercise price of $107 and one year to expiration, we can use the binomial option pricing model. Using a risk-free rate of 12%, the value of the put option is determined to be $0.

Step-by-step explanation:

To calculate the value of a put option, we can use the binomial option pricing model. In this model, we calculate the expected value of the option by taking the weighted average of the possible payoffs. In this case, there are two possible stock prices, $123 and $91, each with a 50% probability. Assuming a risk-free rate of 12%, we can discount the expected payoffs to their present value and calculate the option value.

For the stock price of $123, the payoff of the put option is $107 - $123 = -$16. Discounting this value to the present using the risk-free rate of 12%, the present value is -$14.25.

For the stock price of $91, the payoff of the put option is $107 - $91 = $16. Discounting this value to the present using the risk-free rate of 12%, the present value is $14.25.

Taking the weighted average of the present values, we have (0.5 * -$14.25) + (0.5 * $14.25) = $0. Therefore, the value of the put option with an exercise price of $107 is $0.