1. The value Max[0, X(1 + r)-T - S0] was shown to be the lowest possible value of a European put. Why is this value irrelevant for an American put?
2. Why do higher interest rates lead to higher call option prices but lower put option prices?
3. Suppose a European put price exceeds the value predicted by put-call parity. How could an investor profit? Demonstrate that your strategy is correct by constructing a payoff table showing the outcomes at expiration.