Encyclopedia Inc. want to study the mechanism of equilibrium settings in S & P 500. Considering the statistics, the Spot S&P 500 is currently at 4,000, annual dividend yield of V — the normalized volatility is OA = 0.35, the risk-free rate is 5%. The call and put option based on European setting has exercise price of 2,500 with expiry of 180 days

Calculate the option prices under American and European settings using dividend adjusted binomial model for n = 200 subperiods.