Question

You are attempting to value a put 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 $127 and a 50% chance of decreasing to $91. The risk-free rate of interest is 10%. Calculate the value of a put option with exercise price $109.

What is the value of the put option?

Answer 1

The value or price of the PUT option under the two state model is calculated based on the assumption that there is no opportunity for arbitrage profit. The value of PUT 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 $109

The return if price goes to $127 and option is not exercised ,so payoff = 0

The return if the price goes down to $91 option is exercised ,so payoff = 109-91 = 18

Thus, the expected return is = PROB. * UPSIDE PAYOFF + PROB. * DOWNSIDE PAYOFF

= 0.5 * 0 + 0.5 * 18 = $ 9

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.

P0 or value of PUT option today = Expected return / ( 1+risk free rate )

= 9 / (1+0.1) = $ 8.18