Forward exchange rate. This problem is about forward contracts in foreign exchange and goes beyond the scope of equity derivatives. The spot exchange rate of the euro is S dollars, i.e. to buy one euro one must pay S dollars. The euro zone yield curve is flat at rEU while the American yield curve is flat at rUS. A forward contract on the euro-dollar is an agreement to receive euros and pay dollars at a pre-agreed date T and exchange rate F.

(a) Starting with €1, find two ways to have dollars in a year’s time by investing or borrowing in either currency and exchanging between currencies through the spot and forward markets. Using an arbitrage argument, establish that the 1-year forward exchange rate of the euro must be:

Can you make a parallel with a relevant forward price formula for a stock or equity index?

(b) Assume rEU = 2%, rUS = 4%, S = $1.30 for €1. What is the 1-year forward exchange rate? Can you also find the 2-year forward exchange rate?

(c) Interpret your results in terms of appreciation or depreciation of the dollar. Find at least one supporting argument for your interpretation and one opposing argument. Assuming both arguments weigh equally on the evolution of the euro-dollar exchange rate through time, what would be your best guess of the exchange rate in a year’s time? Can you find a way to make money if this forecast proves to be accurate? Is this an arbitrage?

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