Forward contracts and firm commitments

Firm commitments: what they share

A firm commitment is a derivative in which both sides are obliged to go through with the deal. Neither can walk away when prices move against them. Forwards, futures and swaps all belong to this family.

Every firm commitment spells out the same basic ingredients. Once these are agreed, the only thing left uncertain is the market price of the underlying when the exchange happens.

• A specific underlying (a commodity, currency, share, index or interest rate).
• A specific contract size.
• One or more future dates on which cash or the underlying is exchanged.
• A price for the exchange, agreed today.

How a forward works

A forward contract is an over-the-counter (OTC) agreement between two parties. The buyer agrees to purchase the underlying from the seller at a fixed price on a set future date. The buyer holds a long position and gains if the underlying rises; the seller holds a short position and gains if it falls.

We write the agreed price as $F_0(T)$: the subscript 0 is the date the price is set, and T in brackets is the date of the exchange. The underlying's market price at maturity is $S_T$.

Being OTC, a forward can be tailored to the user's exact needs: any size, any date, any grade of underlying, any credit terms. That makes forwards popular with end users hedging a known exposure, such as an importer who must pay a supplier in foreign currency in three months. The price of this flexibility is counterparty credit risk: each side depends on the other actually paying.

At inception neither party pays anything. The forward price is set so that the deal is fair to both sides on day one.

Compare with buying the asset now: to get the same exposure in the cash market you would pay $S_0$ today and earn $S_T - S_0$. The forward gives you the same price exposure without paying anything up front.

Payoff at maturity

At T the buyer must pay $F_0(T)$ for something worth $S_T$. Her payoff is therefore $S_T - F_0(T)$. If the market ends above the forward price she gains; if it ends below, she loses. The seller's payoff is the exact opposite, $F_0(T) - S_T$.

Since no premium was paid at inception, payoff equals profit for a forward. The breakeven point is simply $S_T = F_0(T)$, where the settlement is zero for both sides.

The payoff is a straight line in $S_T$ with a slope of +1 for the buyer and −1 for the seller. Gains and losses are symmetric: each extra unit the price rises adds one unit to the long's payoff and takes one unit from the short's. This is why firm commitments are called linear derivatives.

Notice what does not matter: today's spot price $S_0$. Settlement compares the price at maturity with the forward price, nothing else.

Delivery or cash settlement

A forward can be physically settled: the seller delivers the underlying and the buyer pays $F_0(T)$. Or it can be cash settled: only the difference changes hands. The loser pays the winner $|S_T - F_0(T)|$ per unit.

Both methods leave each party in the same economic position. With cash settlement the buyer who wants the physical asset simply buys it in the market at $S_T$; combined with the cash received or paid, the net cost is still $F_0(T)$.

A forward usually involves a single exchange on one future date. That is one of the features that separates it from a swap, which is a series of exchanges.