Valuing Forward and Futures Contracts
The forward or futures price of an investment asset that provides no income is given by
where S0 is the spot price of the asset today, T is the time to maturity of the forward or futures contract, and r is the continuously compounded risk-free rate for maturity T. When the asset provides income during the life of the contract that has a present value I, this becomes
When it provides a yield at rate q, it becomes
A foreign currency can be regarded as an investment asset that provides a yield equal to the foreign risk-free rate, so that the forward or futures price for a foreign currency is
where rf is the foreign risk-free rate (continuously compounded) and S0 is the spot exchange rate. The value of a forward contract where the holder has the right to buy the asset for a price of K is, in all cases
where F is the forward price. The value of a forward contract where the holder has the right to sell the asset for a price of K is similarly ...