Consider an 8-month put option on the s&P 500 struck at K-2100. The current price is S-2050, the risk-free rate is 3%, and the dividend yield on the index is 2%. Use a four-period binomial tree (with CRR values of u and d) to price the option using a volatility of 15%. Value the option supposing it is American. Be sure to indicate when early exercise is optimal, if ever.