Show that if c is the price of an american call with

Question

Show that, if C is the price of an American call with exercise price K and maturity T on a stock paying 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

where S₀ is the stock price, r is the risk-free 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^-rT invested at the riskfree rate

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