The S&P 500 spot level is 2,475. The 1-year at-the-money call on is selling at $140. The risk-free rate is 5% and the index pays a dividend yield of 3.5%. The S&P 500 options are European.

a) What is the theoretical price of the 1-year at-the-money put price. 

b) The 1-year put is selling at $80 on the market, show how you can benefit from this arbitrage opportunity. Show all detail.

c) If the S&P 500 options were American, will there be an arbitrage opportunity?