Question

Consider a three-year European call option with the strike price of $150. The underlying stock will pay $10-dividend two years later from now. The current stock price is $170. The risk-free rate is 3% per annum. Find the range of the call prices that do not allow any arbitrage.

Answer 1

Upper bound for a call option is the stock price which is $170.

Lower bound for the call option is max(S0 - Ke^(-rT) - De^(-rt), 0) = max(170 - 150*e^(-3%*3) - 10*e^(-3%*2), 0) = max(42.33, 0) = 42.33

Range of call prices for which there will be no arbitrage are from $42.33 to $170.