Consider a 1-week (i.e., 1/52 year) futures put option on a stock index with strike price $4080. The current futures price of the index is $4100. The risk free interest rate is 1% per year with continuous compounding. The volatility of the index futures is 20%. (1). Assume that the futures put is of European style. Compute the futures put price. Using the put-call parity, compute the price of a European futures call on the index with the same strike and maturity. (2). Assume that the futures put is of American style. Approximate the futures put price using a 2-step binomial model