Show that if C is the price of an American call with strike price K and maturity T on a stock providing a dividend yield of q, and P is the price of an American put on the same stock with the same strike price and exercise date, then Soe~"T -K^C-P^S0- Ke~rT where So is the stock price, r is the risk-free interest rate, and r > 0. (Hint: To obtain the first half of the inequality, consider possible values of:

Portfolio A: a European call option plus an amount K invested at the risk-free rate;

Portfolio B: an American put option plus e~qT of stock, with dividends being reinvested in the stock.

To obtain the second half of the inequality, consider possible values of:

Portfolio C: an American call option plus an amount Ke~^T~^ invested at the risk-free rate;

Portfolio D: a European put option plus one stock, with dividends being reinvested in the stock.)