Question

Suppose AT&T’s current stock price is $100 and it is expected to either rise to 130 or fall to 80 by next April (assume 6-months from today). Also assume you can borrow at the risk-free rate of 2% per 6 months. Using the binomial approach, what would you pay for a call option on AT&T that expires in 6-months and has a strike price of $105? A strike price of $110?

Answer 1

Strike price is $105

If the price is $130 in six months, the call option payoff = 130 - 105 = $25

If the price is $80 in six months, the call option payoff = 0 because the option is out of the money

The expected payoff = 25 * 0.5 + 0 * 0.5 = $12.5

Call option price = 12.5/(1 + 0.02)

Call option price = $12.2549019608

Strike price is $110

If the price is $130 in six months, the call option payoff = 130 - 110 = $20

If the price is $80 in six months, the call option payoff = 0 because the option is out of the money

The expected payoff = 20 * 0.5 + 0 * 0.5 = $10

Call option price = 10/(1 + 0.02)

Call option price = $9.8039215686