Calculation of Payoffs from Forward Contracts:
This example will help us understand it better, two parties might agree today to exchange 500,000 barrels of crude oil for US $ 42.08 a barrel three months from today.
A forward contract is specified with four variables:
1) the underlier,
2) the notional amount n,
3) the delivery price k, and
4) the settlement date on which the underlier and payment will be exchanged.
In our example, oil is the underlier. The notional amount is 500,000 barrels. The delivery price is US $ 42 per barrel. The settlement date is the actual date three months from now when the oil will be delivered in exchange for a total payment of US $ 21.04 MM.
The party who receives the underlier is said to be long the forward. The other party is short. At settlement, the forward has a market value given by n(s - k).
where s is the spot price of the underlier at settlement. This formula derives from the fact that, at settlement, the long party is paying a delivery price k for an underlier then trading at price s. The difference between those two prices, multiplied by the
notional amount, is the market value of the forward. Formula tells us that forwards have linear payoffs.
A forward may be cash settled, in which case the underlier and payment never exchange hands. Instead, the contract settles with a single payment for the market value of the forward at settlement, as given by 1. If the market value is positive, the short party pays the long party. If it is negative, the long party pays the short party. Suppose the forward in our oil example were cash-settled. On the settlement date three months from today, no oil would change hands, and there would be no payment of US $ 21.04MM. If the spot price at settlement were, say, US $ 47.36, then the forward would settle with a single payment of
500,000(47.36 - 42.08) = US $ 2.64MM
made by the short party to the long party.
Forward are generally quoted as delivery prices, which are called forward prices. Forward prices fluctuate with market conditions. When a forward is entered into, the contract's delivery price is set equal to the quoted forward price. That delivery price then remains fixed until the forward settles. For example, a dealer might quote a three-month oil forward at 41.25/41.29. Those are the bid and offer forward prices. If a counterparty accepts the offer price for 500,000 barrels, then the delivery price on that contract will be USD 41.29.
Issues such as the time value of money, short-term supply and demand, market expectations of future spot prices and cash-and-carry arbitrage tend to make forward prices diverge from spot prices, but relevant factors vary from one market to the next. A graph of forward prices for different maturities is called a forward curve.