2.12. Show that if C is the price of an American call with exercise price X 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,

where So 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 X invested at the risk-free rate Portfolio B: an American put option plus eat of stock with dividends being re- invested in the stock To obtain the second half of the inequality, consider possible values of:

Portfolio C: an American call option plus an amount Xe rate invested at the risk-free Portfolio D: a European put option plus one stock with dividends being reinvested in the stock)

Transcribed Image Text:

- Soe TXC-P