1. Consider stock with a current price (St ) of $100 and a constant annualized return volatility () of 20%. The stock does not pay dividends. A risk-free zero-coupon bond with $1 par and one year maturity is worth $0.95 today.

   (a) (10) Using the approach discussed in class, construct a two-step binomial tree to approximate the stock price dynamics, with each step being 1 year. List the stock price at each node at one and two years. (b) (5) Compute the risk-neutral probability of going up and going down at each step. (c) (20) Based on the binomial tree, compute (i) the current value and (ii) the delta of an European put option on the stock with a maturity of two years and a strike price of $110. (d) (10) Based on the binomial tree, compute (i) the current value and (ii) the delta of an American put option on the stock with a maturity of two years and a strike price of $110.