4) 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 three months. The risk-free interest rate is 8%.

a) Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.

b) Explain carefully the arbitrage opportunities if the American put price is greater than the calculated upper bound.