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EXERCISE 4 Consider a stock that pays no dividend in an N-period binomial model. A European call has payoff CN = (SN-K) at time N. The price of this call at earlier times is given by the risk-neutral pricing formula: G = En [e--(N16cx), n=0,1,...,N - 1. Consider also a put with payoff PN = (K-S) at time N, whose price at earlier times is Pn= E. [e--(N-16 pn, n=0,1,...,N- 1. Finally, consider a forward contract to buy one share of stock at time N for K dollars. The payoff of the forward contract at time N is fn = SN-K, and its price at earlier times is In = , [er(N-1) ]. n = 0,1,..., N - 1. 1. If at time zero you buy a forward contract and a put, and hold then until expiration, explain why the payoff you receive is the same as the payoff of a call, i.e., explain why CNN + PN. 2. Show (rigorously) that for every n it holds that c = + P 3. Using the fact that the discounted stock price is a P-martingale, show (rigorously) that fo - So- e k 4. Suppose you begin at time zero with fo, buy one share of stock, borrowing money as necessary to do that, and make no further trades. Show that at time N you have a portfolio valued at N. 5. Show that, at time zero, the price of a call with strike equal to the forward price is the same as the price of a put with strike equal to the forward price. 6. For a strike equal to the forward price as in the previous question, do we have for every n