2 0 0 0 da:; dao where is a risk-neutral probability of the event that the exchange rate goes up in a month, u and d are parameters of the binomial model such that u > (1 +r) > d > 0, and r = 0.006 is the risk free monthly rate Suppose that a US producer gets his input from a European supplier and has to pay for the input in . The next payment is due in two months from now and amounts to 30,000. To reduce his exposure to exchange rate risks. the American producer buys the futures contracts. Each contract guarantees delivery of 1,000. The arbitrage free futures prices are = $1.200. $ 1.240, and d = $1. 160. Here is the spot delivery price for the futures with 2 months maturity: 1u (respectively, 1a) is the delivery price next month for the futures of 1 month maturity if the exchange rate goes up (respectively, down). To find prices for delivery of 1, you need to divide the above prices by 1,000 (a) Write down the equation for the risk neutral measure (T. 1-7) and find the risk neutral probabilities as functions of u, d, and r (b) Write down the equations for the futures prices for delivery of 1 in terms of the corresponding exchange rates and find risk neutral proba- bilities, parameters u and d, and the spot rate ro. You are not allowed to make any shortcuts here! (c) Draw a tree that represents the exchange rate dynamics for the values you calculated in (b) (d) Now, assume that the American producer buys 30 shares of a European call option: each of these contracts gives the producer the right (but not the obligation) to buy 1,000 in two months from now for the strike price S1,170. Calculate the arbitrage free value of the European call at each spot and describe the evolution of the call value using a time- decision tree