Econ 369F Practice test for midterm II Fall 2022 Svetlana Boyarchenko This practice test has the format of the 2nd midterm. You have a 24 hour window for this submission. You will need to take pictures of your answers to upload them to Gradescope. You will see my solutions to the practice test after all submissions have been made. Then you will be given a 24 hour window for submission of the midterm exam. A weighted average between the practice (30%) and actual (70%) test will be your midterm grade. Please read all the questions carefully. You can earn a total of 30 points on the test. You must show all your work to get full credit. Partial credit will be given at my discretion, and it is non-negotiable. Good luck! Question 1 (15 points) Consider a two-period economy under uncertainty, where all accounts are settled in USD. Suppose that the current exchange rate between Euro and USD is e1=$1.10. The future exchange rate dynamics is represented by the following tree: $1.14 $1.12 1 $1.10 $1.10 1 $1.10 $1.08 1 $1.06 t = 0 t = 1 t = 2 where = 0.6 is a risk-neutral probability of the event that the exchange rate goes up in a month. Assume that the risk free monthly rate is r = 0.005. (a) Suppose that a US producer sells his output to a European retailer and gets paid in Euro. The next payment is due in two months from now and amounts to e200,000. To reduce his exposure to exchange rate risks, the American producer sells the futures contracts. Each contract guarantees 2 delivery of e1,000. Find arbitrage free futures prices 0, 1. Describe the evolution of the producer's cash streams using a time-decision tree. (b) Suppose that instead of receiving e200,000 in two months from now for the whole output, the American producer requires a pre-payment of e100,000 in a month from now, so that he receives e100,000 each month for two months in a row. To reduce his exposure to exchange rate risks, the producer enters a swap contract: namely, he locks the exchange rate at X at t = 0. The notional amount of the swap contract is e100,000 per month. The producer locks his profits of $100,000X per month: each month on the settlement day, the producer gets e100,000 from the retailer, sells the payment for $US at the spot exchange rate, and also receives from or pays to the supplier the difference between the spot exchange rate and X times 100,000. Calculate the arbitrage free value of X. Describe the evolution of the producer's cash streams using a time-decision tree. medbreak (c) Now, assume that the American producer buys 200 shares of a European put option: each of these contracts gives the producer the right (but not the obligation) to sell e1,000 in two months from now for the strike price $1,110. Calculate the arbitrage free value of the European put at each spot and describe the evolution of the put value using a time-decision tree. Question 2 (15 points) Consider a two-period (t = 0, 1) market with two assets: a risk free bond with face value $1 and rate of return r = 0.1; and a stock, whose current price is q0. The future price q1 is uncertain, and it can take one of the two values q1 {qh, ql}, where qh > q0(1 + r) > ql . (a) Suppose that qh = $120 and ql = $90. An investor uses the past stock price dynamics to estimate that the probabilities of the stock price q1 taking either of the values are 50:50. Therefore, she evaluates the current stock price as q0 = 0.5qh + 0.5ql 1 + r = 110 1.1 = $95.44. The investor observes that the current price of the stock, is not $95.44, but $98.18, and decides that the stock is overpriced by the market. Is the investor right? Explain why or why not. (b) There is also the European call option on the stock with the strike $100 and maturity date at t = 1. What is the payoff on the option at t = 1? Create a replicating portfolio for the call and calculate the option price at t = 0. (c) Show that if the option price is different from the value you found in (b), then it is possible to create an arbitrage portfolio. (d) Consider the American put option on the stock with the maturity date t = 1 and the strike 90 < K < 120. For which values of K the option will be exercised prematurely?