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Subject 6. Currency Forward and Futures Contracts
This subject is optional.

The pricing and valuation of currency forwards is remarkably similar to that of equity forwards.

F(0, T) = [S0/FVf,T(1)] FVd,T(1)

where:

• S0 is the current spot exchange rate (direct quote: # of domestic currency/ one unit of foreign currency)
• FVf,T(1) is the future value of 1 unit of foreign currency, based on the foreign interest rate.
• FVd,T(1) is the future value of 1 unit of domestic currency, based on the domestic interest rate.

The term in brackets is the spot exchange rate discounted by the foreign interest rate. This term is then compounded at the domestic interest rate to the expiration day.

This formula is called interest rate parity. It states that:

• The forward rate premium (or discount) of a currency should reflect the differential in interest rates between the two countries.
• The discounted interest rate differential equals the percentage of the forward discount.

It is equivalent to the statement that one unit of foreign currency, deliverable on a particular future date, must cost the same amount independently of whether it is obtained through the forward market or by means of the spot market. The differences in the spot and forward rates for currencies are due solely to differentials in interest rates.

For example, if one-year interest rates are 5% in the U.S. and 10% in the U.K. and the current spot exchange rate in dollars per foreign currency is 2, the one-year forward rate will be 1.91. The 5% interest rate advantage that could be obtained in the U.K. will be offset by a 5% depreciation in the value of the pound. As pounds are bought spot and sold forward, the forward discount will widen. Simultaneously, as money flows from the U.S., interest rates here will tend to rise while the inflow of funds to the U.K. will tend to depress interest rates there.

The value of a currency forward contract is the present value of the difference in forward prices.

Vt(T) = PVd, t, T[Ft(St, T) - F0(S0, T)]

Or it is simply the spot rate discounted at the foreign interest rate over the life of the contract, minus the present value of the forward rate at expiration. Assume non-continuous-compounding:

Vt(0, T) = St/(1 + r(f))(T-t) - F(0, T)/(1 + r)(T-t)

where:

• r(f) is the foreign interest rate.
• r is the domestic interest rate.