Calibrating the Exchange Rate Process (10 Points) Table 1: On April 6th, 2021, according to investing.com, the spot price of the exchange rate is $1.1875, while the quotes for the EUR/USD forward contracts are given in the table below. Name EURUSD 1M FWD EURUSD 2M FWD EURUSD 3M FWD EURUSD 4M FWD EURUSD 5M FWD EURUSD 6M FWD EURUSD 7M FWD EURUSD 8M FWD EURUSD 9M FWD EURUSD 10M FWD EURUSD 11M FWD EURUSD 1Y FWD Bid 7.22 14.59 22.38 30.1 38.02 45.93 53.99 61.7 76.45 84.84 92.49 101.24 Ask High Low 7.7 7.64 7.5 14.83 14.75 14.72 22.74 22.59 22.63 30.7 30.51 30.56 38.42 38.1 38.3 48.09 46.93 46.52 54.91 56.15 54.53 62.91 61.95 62.48 78.45 77.28 77.71 85.74 84.98 85.43 93.49 93.91 93.26 103.37 102.12 102.51 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 x exp (( (10 - )+oB-) (2) where 0=r - ry denotes the difference between the US risk-free rate and the EU risk-free rate. o is the annual volatility of the exchange rate B7 ~ N(0,7) is a standard Brownian motion Your first task is to calibrate the GBM: 6 (a) For 0, you need to refer to the interest rate parity and estimate 0 using the forward quotes from Table 1. Note that this a "forward-looking approach. (5 Points) (b) For o, you need to download data for the daily EUR/USD exchange rate using the EU- RUSD=X symbol from Yahoo Finance. Your data should be daily and range between 2018- 01-01 and 2021-04-05. Given the adjusted prices, you need to calibrate o 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 28 bps, for instance. Calibrating the Exchange Rate Process (10 Points) Table 1: On April 6th, 2021, according to investing.com, the spot price of the exchange rate is $1.1875, while the quotes for the EUR/USD forward contracts are given in the table below. Name EURUSD 1M FWD EURUSD 2M FWD EURUSD 3M FWD EURUSD 4M FWD EURUSD 5M FWD EURUSD 6M FWD EURUSD 7M FWD EURUSD 8M FWD EURUSD 9M FWD EURUSD 10M FWD EURUSD 11M FWD EURUSD 1Y FWD Bid 7.22 14.59 22.38 30.1 38.02 45.93 53.99 61.7 76.45 84.84 92.49 101.24 Ask High Low 7.7 7.64 7.5 14.83 14.75 14.72 22.74 22.59 22.63 30.7 30.51 30.56 38.42 38.1 38.3 48.09 46.93 46.52 54.91 56.15 54.53 62.91 61.95 62.48 78.45 77.28 77.71 85.74 84.98 85.43 93.49 93.91 93.26 103.37 102.12 102.51 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 x exp (( (10 - )+oB-) (2) where 0=r - ry denotes the difference between the US risk-free rate and the EU risk-free rate. o is the annual volatility of the exchange rate B7 ~ N(0,7) is a standard Brownian motion Your first task is to calibrate the GBM: 6 (a) For 0, you need to refer to the interest rate parity and estimate 0 using the forward quotes from Table 1. Note that this a "forward-looking approach. (5 Points) (b) For o, you need to download data for the daily EUR/USD exchange rate using the EU- RUSD=X symbol from Yahoo Finance. Your data should be daily and range between 2018- 01-01 and 2021-04-05. Given the adjusted prices, you need to calibrate o 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 28 bps, for instance