Exercise 1. Consider a three period binomial model (one initial date and two steps) as in class. Let the initial stockprice be $100. Let the upward increments be u = 1:2 and the downward be d = :9. Thus, the up-up stateshould have Suu = u u S0 = 1:2 1:2 100 = 144 and so on. The risk free rate is ten percent per period.
The call option with strike price of $100 was priced in class.Exercise 1. Price the put option with strike price of $100 using replicating portfolios. Does put-call parityhold (remember the interest accrues in discrete steps)? Explain.
Exercise 2. Suppose we had a futures contract to buy one share of the stock at the nal date at price F0.The stock price today is S0. The stock price tomorrow will either be Su or Sd. There is a risk free bondthat gets rate r.
What premium should the futures contract have today?
In other words, use the binomialmodel to price this contract.In the market, F0 will be chosen so that the premium exchanged at date 0 is $0. What futures pricewould give that?
Use this to come up with the futures price at each node in the binomial tree in the previousproblem. At each of these states (0, u, or d) is the market in contango or normal backwardation?