Pricing Currency Futures

• Currency futures are priced in the same manner as currency forward contracts.
• Price of a Currency Future with Simple Compounding:

f(0,T)X/Y = S0,X/Y ((1+rX)/(1+rY))T

• T = total contract length

• S0 = Spot exchange rate for X/Y (#X units domestic per 1Y foreign) at initiation

• rX = Risk free rate in country X (domestic currency)

• rY = Risk free rate in country Y (foreign currency)

• Price of a Currency Future with Continuous Compounding

f(0,T)X/Y = (S0,X/Y e-ryT ) erxT

• If the currency future is not "fairly" priced (i.e. not priced based on an arbitrage relationship based on risk free rates), then it is possible for a trader to earn a risk-free arbitrage profit.
• Futures Market Overvalues a Currency:

1. Sell the overvalued futures contract
2. Buy the underlying currency in the spot market
3. Borrow and invest all cash flows