Question

8. Derivatives 8a. What is a lower bound for the price of a two-month call option on a non-dividend-paying stock when the stock price is $29, the strike price is $24, and the risk-free interest rate is 4% per annum? 8b. Please show the arbitrage strategy if the price of this option is below the lower bound. 8c. What if there is a $3 cash dividend in 1 month, what would be the new lower bound?

Answer 1

Lower bound is given by max(So-Ke^rt,0)

A)

Details provided : So = 29, K =24, Rf = 4%, T = 2

Lower bound = max(29-24*e^(4%*2/12),0) = 4.84

B)

If call option is below 4.84 an investor can purchase the call at this lower price and exercise the call option 2 months later and get risk free return

C) If there is a cash dividend of 3 in next 1 month new lower bound is

Lower bound = 4.84 - 3*e^(-4%*1/12) = 1.849449