Show that, if C is the price of an American call with exerci
Question and Solution
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
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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 S0eqT K < C P < S0 KerT; 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 eqT 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 KerT invested at the riskfree rate Portfolio D : a European put option plus one stock with dividends being reinvested in the stock.)
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