Forward and Futures Pricing and Hedging › Forward Contract Mechanics

Before diving into pricing theory, we need to understand exactly what happens when you enter a forward contract and what payoffs result at expiration. The mechanics of these contracts form the foundation upon which all pricing and hedging analysis rests. By carefully examining how money flows at different points in time, we develop the intuition necessary for understanding why forward prices take the values they do.

When you enter a forward contract to buy an asset at price $F$ at time $T$, you are said to be long the forward. At expiration, you pay $F$ and receive an asset worth $S_T$ (the spot price at maturity). The payoff calculation is straightforward: you compare what you paid to what you received. Since you paid $F$ and received something worth $S_T$, your net gain or loss is simply the difference:

$$\text{Long forward payoff} = S_T - F$$

where:

• $S_T$: spot price of the asset at expiration
• $F$: agreed-upon forward price

This formula captures the essence of your position. If the asset price rises above the forward price, you profit because you locked in a purchase price lower than the prevailing market value. If it falls below, you lose because you committed to buying at a price higher than where the market ultimately settled. The payoff is linear in the spot price, meaning every dollar increase in $S_T$ translates directly into a dollar of profit, and every dollar decrease translates directly into a dollar of loss.

The short position (the party who agreed to sell) has the opposite payoff, which follows logically from the zero-sum nature of forward contracts:

$$\text{Short forward payoff} = F - S_T$$

where:

• $F$: agreed-upon forward price
• $S_T$: spot price of the asset at expiration

The short position profits when prices fall below the forward price because they locked in a sale price above market value. They lose when prices rise because they must deliver an asset worth more than the payment they receive. Whatever the long position gains, the short position loses, and vice versa.

Notice the linear payoff profiles evident in the chart. Unlike options, which provide asymmetric protection, forwards have symmetric profit and loss potential. The long benefits dollar-for-dollar from price increases and loses dollar-for-dollar from price decreases. There is no cap on potential gains and no floor on potential losses. This symmetry reflects the unconditional nature of the forward commitment: both parties are obligated to complete the transaction regardless of where the market moves.

A critical feature of forward contracts is that no money changes hands at initiation. The forward price $F$ is determined precisely so that the contract has zero value to both parties at the outset. This distinguishes forwards from options, where the buyer pays a premium upfront for the right (but not obligation) to transact.

The zero-initial-value property might seem arbitrary at first glance, but it follows directly from how markets establish forward prices through the forces of supply and demand. If a forward contract had positive value to the long at initiation, everyone would want to be long, and no one would willingly take the short side. This imbalance would drive the forward price up as longs compete for contracts, continuing until the advantage disappeared. Similarly, if the contract had positive value to the short, everyone would want to sell forwards, driving the price down. The forward price adjusts until neither party has an advantage, reaching an equilibrium where both sides view the contract as a fair exchange of risk.

This equilibrium condition provides the starting point for our pricing analysis. We don't need to model supply and demand explicitly; instead, we can use arbitrage arguments to determine what the forward price must be to ensure the contract has zero initial value. This approach leads us to the cost-of-carry model.