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# Futures on Exchange Rates

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Suppose you are trading Forex (Foreign exchange) now, and the spot price is EUR:USD=1.40:1. The risk free rate of EUR is 3% while risk free rate of USD is 1%

(a) Hypothetically, what is the theoretical future price of EUR:USD, which will mature in 2 yrs in the future?

(b) Now suppose the EUR:USD future contract mature in 2 yrs is currently traded at 1.45:1 in futures market, what should you do to arbitrage? (To lock your profit, buy what and sell what?)

(c) Suppose you are holding the long EUR position and want to hedge your risk by using futures. Assume the volatility of futures is 2 times of spot price, and the correlation of futures and spot is +0.9, the future contract is \$100,000 per contract. How many contracts do you need to buy/sell to hedge your 1 billion dollars position?

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#### Solution Preview

Please see attached file:
Suppose you are trading Forex (Foreign exchange) now, and the spot price is EUR:USD=1.40:1.  The risk free rate of EUR is 3% while risk free rate of USD is 1%
(a) Hypothetically, what is the theoretical future price of EUR:USD, which will mature in 2 yrs in the future?

Forward rate = Spot rate x e ^{ (risk free rate of Euro- risk free rate of dollar) x time to maturity}
where e is the exponential function

Or Forward rate = 1.40 x e ^{ ...

#### Solution Summary

Calculates theoretical future price and arbitrage profit.

\$2.49