Suppose that Stock XYZ is currently trading at $20 and is expected to pay a dividend of $0.50 per share in 5 months and again in 10 months. Assume that annual continuously compounded interest rate is 6% and the volatility of the stock is 30% per year.
a. Find the price of a 1-year American call option written on this stock with a strike of $18 using BSM Model.
b. Find the price of a 1-year American put option written on this stock with a strike of $18 using BSM Model.
c. Find the delta of the call and put options.