Question

A stock with a stock and exercise price of $20 can either increase to $26 or decrease to $18 over the course of one year. In a one-period binomial option model, given an interest rate of 5% and equal probabilities, what is the likely put option price? (Use annual compounding.)

a. 2.00

b. 0.95

c. 1.00

d. 1.90

The instructor said the answer is B but how?

Answer 1

When the stock price is $26, the put option is out of the money because the stock price > exercise price ($20). So, the payoff is 0.

When the stock price is $18, the put option is in the money because the stock price < exercise price. So, the payoff = 20 - 18 = $2

The expected payoff with equal probability of 0.5 = 0 * 0.5 + 2 * 0.5 = $1

The present value of the expected payoff is the put option price

Put option price = 1/(1 + 0.05)^1

Put option price = 0.9523809524

Put option price = $0.95