Consider a two-step binomial model for a stock index with dividend yield 1.005%. The current index value is $1000. In a 1-year period, the index value either goes up by 10% or goes down by 10%. The risk free interest rate is 1.005% per year with continuous compounding. (1). (4 points) What's the price of a 2-year at-the-money American vanilla put option? (2). (1 point) When should the put be early exercised?