Todays date is Nov 8th, 2021, and a U.S. exporter has been promised a payment of 1,250,000 euros in May 1st, 2022. The spot exchange rate on Nov 8th, 2021 is $1.1594. According to the Chicago Mercantile Exchange (CME Group), the exporter can trade EUR/USD contracts with face amount of 125,000 euros that will expire in June 2022. The CME Group states that futures contracts are terminated on the second business day immediately preceding the third Wednesday of the contract month. Calibrating the Exchange Rate Process (10 Points) Table 1: On Nov 8th, 2021, according to investing.com, the spot price of the exchange rate is $1.1594, while the quotes for the EUR/USD forward contracts are given in the table below. The data set is available via the forward.csv file. Name Bid Ask High Low EURUSD 1M FWD 6.36 6.52 6.44 6.37 EURUSD 2M FWD 19.64 19.73 19.68 17.46 EURUSD 3M FWD 25.71 28.51 27.09 26.26 EURUSD 4M FWD 33.68 34.13 33.77 33.39 EURUSD 5M FWD 41.66 42.26 41.82 41.27 EURUSD 6M FWD 48.22 50.22 49.17 48.27 EURUSD 7M FWD 56.8 58.04 57.33 56.61 EURUSD 8M FWD 65.87 67.13 66.26 64.77 EURUSD 9M FWD 74.37 75.27 74.86 71.69 EURUSD 10M FWD 84.35 85.31 85.26 80.79 EURUSD 11M FWD 94.11 95.11 94.94 90.35 EURUSD 1Y FWD 103.97 105.17 104.9 99.55 1. Let St denote the EUR/USD exchange rate, i.e. the amount of dollars needed to purchase a single Euro at time t. Under no-arbitrage pricing (risk-neutral valuation), St follows a Geometric Brownian Motion (GBM), such that the future spot price is given by ST = St exp ( 2 2 ) + B ! (2) where = r rf denotes the difference between the US risk-free rate and the EU risk-free rate. is the annual volatility of the exchange rate B N(0, ) is a standard Brownian motion Your first task is to calibrate the GBM: 4 (a) For , you need to refer to the interest rate parity and estimate using the forward quotes from Table 1. Note that this a forward-looking approach. (5 Points) (b) For , you need to download data for the daily EUR/USD exchange rate using the EURUSD=X symbol from Yahoo Finance. Your data should be daily and range between 2018- 01-01 and 2021-11-05. Given the adjusted prices, you need to calibrate using the historical returns. Note that this calibration is backward-looking, which is in line with what you did in Project 1. (5 Points) Hint: For foreign exchange rates, it is common to relate to the interbank lending rate in terms risk-free rate. For instance, see the USD and EUR LIBOR rates according to the market data from Wall Street Journal available here. According to that week, the 1-Year Libor rate for USD is 36 bps, for instance. VaR for the Unhedged (5 Points) 2. Assume that the exporter does not hedge the exchange rate risk. In this case, the exporter exchanges the euros on the spot market upon receiving the payment in the future. Let VT denote the profit/loss (P&L) of the exporter at delivery time, which is given by ST St . What is the 99% VaR of the exporters P&L in $? (5 Points) Recall that if VT denotes the P&L at time T, then the 1 VaR is V aRt(VT , ) = Et [VT ] Qt(VT , ) (3) Hint: The answer is greater than $100K. If the euro weakens relative to the dollar, then the exporter gets paid less dollars in the future. Given that the exporter expects 1.25M euros, the future P&L depends on the future spot rate. You need to solve this question using a MC simulation. Unitary Hedge (10 Points) 3. Consider a unitary hedge, in which the exporter shorts 10 futures contracts today and closes the position when the euro payment is received. If the risk-free rates are fixed and there is no arbitrage, the price of the futures contract should obey to the interest rate parity. In other words, the futures contract price at time t is given by Ft = St e (rrf )(tdt) (4) with td denoting the maturity time of the futures contract. Assume that there is no transactions cost, i.e. you are able to buy and sell futures contract with respect to the price implied by the interest rate parity. Using a MC simulation, address the following: 5 (a) What is the 99% VaR of the P&L with unitary hedging? (5 Points) (b) Suppose instead you use the futures contract expiring in March 2022 (before delivery). What is the 99% VaR of the P&L now? Elaborate in terms of basis risk (5 Points) Hedging using ETFs (5 Points) 4. Suppose for some reason the exporter decides to use ETFs (or ETNs) to hedge currency exposure instead of using futures or forward contracts. Your task is to screen 5 different ETFs. For each ETF, provide an economic rationale behind each to serve as a EUR/USD hedge. Justify your reasoning by reporting the hedge effectiveness of each instrument. Note this is an open question without a unique answer. However, your reasoning should make sense in terms of economic mechanisms behind the EUR/USD exchange rate movement.

In R please!