The S&P 500 spot level is 4,500. The 1-year at-the-money call on is selling at $150. The risk-free rate is 5% and the index pays a dividend yield of 2%. 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 $10 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?