A 3-months European call is $3, put is $2 in February. The stock price is $43, the strike price is $46, and a dividend of $1 is expected in 1 month, the zero coupon bond is $46. The risk-free interest rate is 10% per annum for all maturities. Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date. Explain carefully the arbitrage opportunities