Explain carefully the arbitrage opportunities in Problem if the American put price is greater than the calculated upper bound.
Problem :
The price of an American call on a non-dividend-paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in 3 months. The risk-free interest rate is 8%.
Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.