Financial Economics. Show all work and formulas used.

Exercise 1. In a three period (two step) binomial model with u = 1.05, d = .9, and r = .05 price a call option and a put option using replicating portfolios. Does put-call parity hold? Exercise 2. What happens to the hedge ratio as the stock price goes up? What happens as it goes down? lim A =?; lim A =? (1) S)oo 5)0 Exercise 3. A stock will either go up to uS or down to dS next period. The risk-free rate is 7'. Use replicating portfolios to derive the premium on a futures contract with futures price F. What would the futures price need to be for this premium to equal zero? Exercise 4. Use Excel or similar for this exercise. Get monthly prices on one stock, the current T-bill rate, and the premium, strike, and expiration on at least three options on that stock. Use a binomial model with u, d, and r from the data and at least ten periods to price the options. Use the Black-Scholes equation to price the options. Compare these to the actual price of the options