Forward Contracts in Finance: Principles, Pricing Models, and Practical Applications

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Introduction to Forwards

Forward contracts are fundamental instruments in the world of finance, enabling parties to lock in prices today for transactions that will occur in the future. Whether used to hedge against unpredictable market movements or to speculate on price changes, forwards play a crucial role in managing risk across currencies, commodities, and interest rates. Unlike more standardised futures contracts, forwards are tailor-made agreements negotiated privately between counterparties, offering flexibility but also exposing participants to credit risk. This article introduces the core mechanics of forward contracts, explores how their prices relate to spot markets and interest rates, and examines practical applications such as hedging foreign exchange exposure and managing interest rate risks through Forward Rate Agreements (FRAs). By understanding these concepts, readers will gain insight into why forwards remain indispensable tools for corporations, investors, and financial institutions alike.

The basic concept

A forward contract is a binding agreement between two parties to buy or sell an asset at a predetermined price on a specified future date. In the case of currency forwards, this price is the exchange rate fixed at the time the contract is initiated. For example, Party A might agree to deliver USD 100,000 to Party B at a forward rate of 1.10 USD/GBP, receiving GBP 90,909.09 in return. By locking in this rate, Party A hedges against unfavourable currency movements, ensuring it receives exactly GBP 90,909.09 at settlement.

Beyond hedging, forwards can also be used to speculate on future changes in the spot rate. Suppose the contract's settlement date is 7 August 2025 and, two days prior, the Bank of England unexpectedly cuts its base rate from 5% to 2%, triggering a sharp depreciation in sterling. Party A, having taken a “long” position in sterling at a forward rate F₀ = 1.10 USD/GBP, would observe the spot rate drop to Sₜ = 1.05 USD/GBP. The payoff to A at maturity (i.e. on 7 August 2025) is calculated as:

Payoff_long = (Sₜ – Fₜ) × Notional

Numerically, if the spot rate falls to Sₜ = 1.05 USD/GBP:

Payoff_long = (1.05 – 1.10) × 90,909.09

Payoff_long = –0.05 × 90,909.09

Payoff_long = –4,545.45 USD

Conversely, the counterparty (short sterling) earns a payoff of:

Payoff_short = (Fₜ – Sₜ) × Notional

In this case:

Payoff_short = (1.10 – 1.05) × 90,909.09

Payoff_short = +4,545.45 USD

Hopefully this example illustrates the zero-sum nature of forward contracts: one party's loss is exactly the other party's gain. The reader should now begin to see how forwards are used both for hedging and speculation - explaining their widespread use among market participants, particularly those employing high leverage.

Relation between spot, interest rates and forward prices

Forward contracts do not operate in isolation - their pricing and demand are closely linked to both the spot price of the underlying asset and prevailing market interest rates. To see how this relationship works, consider a stock currently trading at £50, with no dividend payments. If the annual risk-free interest rate is 10%, then the fair one-year forward price (Fₜ₊₁) is determined by the principle of no-arbitrage:

Fₜ₊₁ = £50 × (1 + 0.10) = £55

The no-arbitrage condition ensures that the cost of buying and holding the stock (financed at the risk-free rate) equals the forward price agreed upon today for delivery in one year. If this relationship fails to hold, arbitrage opportunities arise. That is, traders can lock in risk-free profits by simultaneously buying and selling equivalent cash flows at misaligned prices. This reflects the law of one price, which states that two assets with identical future payoffs must have the same price today.

For example, suppose the forward price is incorrectly quoted at £60 instead of £55. A trader could:

• Borrow £50 at the risk-free rate

• Buy the stock today at £50

• Enter a forward contract to sell the stock in one year for £60

After one year:

• The stock is sold at £60 under the forward contract

• The loan is repaid with interest: £50 × 1.10 = £55

• A risk-free profit of £5 is realised

This arbitrage exists because the quoted forward price (£60) exceeds the fair value (£55), violating the no-arbitrage condition.

The same logic applies when the forward price is too low. Assume the interest rate is still 10%, but the forward price is instead quoted at Fₜ₊₁ = £40. A trader could:

• Sell the stock today at the spot price of £50

• Enter into a forward contract to repurchase the stock in one year at £40

• Invest the £50 proceeds at the risk-free rate

After one year:

• The investment grows to £50 × (1 + 0.10) = £55

• The trader uses £40 to repurchase the stock under the forward

• A risk-free profit of £15 is realised

Again, arbitrage is possible because the forward price is below fair value, violating the no-arbitrage condition.

From this understanding, we can begin to illustrate the payoffs of forward contracts in relation to the spot price at maturity:

Payoff curves for long (panel A) and short (panel B) forward positions

Panel (a) depicts the payoff of a long forward position. Let K represent the agreed delivery price (i.e., the forward price Fₜ₊₁), and Sₜ the spot price at the future date of execution (t + 1). Recall that a long position benefits from a rise in the value of the underlying asset. As the spot price Sₜ rises above the forward price K, the position becomes profitable, since the asset can be purchased at the lower, agreed price and sold at the higher market rate.

More generally, the payoff for a long position is:

Payoff_long = Sₜ – Fₜ

All else equal, as Sₜ increases, the resale value of the asset bought at Fₜ rises, yielding a profit. The same logic applies in reverse for a short position. Here, the trader agrees to sell the asset at the forward price Fₜ at time T. If the market price at that time, Sₜ, is lower than Fₜ, the trader can purchase the asset at the lower market price and deliver it under the contract at the higher forward price. The general payoff from a short position is thus:

Payoff_short = Fₜ – Sₜ

In both cases, the payoff is linear and directly related to the difference between the spot price at maturity and the original forward price, with the direction of the position (long or short) determining whether the trader benefits from a rise or fall in the market price.

Hedging using forward contracts

To illustrate how forward contracts are used for hedging, consider the case of EuroTrade Ltd, a (fictional) European company. On March 15, 2023, EuroTrade knows it will need to pay €8 million to a British supplier on June 15, 2023. To eliminate exchange rate risk, it enters the three-month forward market and agrees to buy pounds at a forward rate of 0.85 GBP/EUR (Fₜ = 0.85). This contract locks in the payment at £6,800,000, regardless of future currency movements.

On the other side of the market, BritExport Inc., a (fictional) UK-based firm expecting to receive €25 million in three months, faces the opposite exposure. To hedge its foreign exchange risk, it sells €25 million forward at 0.8490 GBP/EUR (Fₜ = 0.8490), thereby securing £21,225,000.

While hedging removes uncertainty, it does not guarantee a better outcome. For example, if the spot exchange rate on June 15 turns out to be 0.83 GBP/EUR (Sₜ = 0.83), EuroTrade would have paid only:

€8 million × 0.83 = £6,640,000

had it not hedged. Under the forward contract, however, it pays £6,800,000. The difference can be viewed using the payoff formula:

Payoff_long = (Sₜ – Fₜ) × Notional

Payoff_long = (0.83 – 0.85) × €8,000,000

Payoff_long = –£160,000

In other words, EuroTrade pays £160,000 more than it would have in the spot market. Yet this loss is the cost of certainty - it avoided the risk of potentially worse outcomes.

Conversely, if the spot rate had risen to 0.90 GBP/EUR, the payment without hedging would have been:

€8 million × 0.90 = £7,200,000

In this case, hedging saves EuroTrade £400,000, demonstrating the protection a forward contract can offer.

BritExport’s position mirrors this dynamic. If the spot rate on June 15 is below its forward rate of 0.8490 (e.g., 0.83), the company benefits by selling euros at the higher, locked-in rate. If the spot rate is higher than 0.8490 (e.g., 0.90), BritExport might regret hedging, as it could have received more pounds in the spot market.

This example demonstrates the core objective of hedging: to reduce exposure to adverse movements and provide predictability, not necessarily to maximise returns. This must be so, given even (relatively) small fluctuations in exchange rates - such as a move from 0.85 to 0.83 (a 2.4% change) - can result in significant financial differences when applied to large notional amounts. Hedging helps firms manage this risk in a disciplined, forward-looking way.

Forwards vs Futures: Key Distinctions and Risk Implication

A distinction must be drawn between forwards and their closely related derivative counterpart: the future. Futures will be explored in more detail in a subsequent article (no pun intended). As noted in our introduction, forwards are over the counter (OTC) derivatives - that is, contracts negotiated privately between two parties and not traded on an organised exchange. Each forward is individually tailored, allowing full flexibility in contract size (i.e., the notional amount), settlement date, and delivery terms. This customisation applies to both cash-settled and physically settled forwards.

In contrast, futures are standardised contracts traded on formal exchanges. Each contract has a predefined notional amount, maturity date, and settlement procedure. A key feature of futures is that they are marked to market daily - any gains or losses are settled each day via variation margin payments between the trading parties. Furthermore, most futures are not held to maturity but are instead closed out before expiry through an offsetting trade. The reasoning behind daily settlement and central clearing will be explored in more depth in a future article, as well as issues relating to central clearing parties and their origins.

Another critical distinction lies in the credit risk profile of the two instruments. Forward contracts are typically held to maturity and settled then - either via delivery of the underlying asset or by cash payment. This exposes each party to counterparty credit risk throughout the life of the contract. In contrast, futures contracts materially reduce credit risk due to the role of the clearinghouse and the requirement for daily margining. The exchange clearinghouse becomes the counterparty to every trade and ensures performance by collecting and redistributing margin, effectively insulating each trader from the default risk of their original counterparty.

However, this protection is not absolute. While futures significantly reduce credit risk, they do not eliminate it entirely - particularly in the event of severe market stress or clearinghouse failure.

To illustrate the difference in settlement and credit exposure, consider the following example (pricing mechanics for futures will be addressed in a later article). Assume the 60-day forward price and futures price for the euro are both 1.0800 USD/EUR.

Suppose trader X enters a €2 million forward contract, taking a long position. Meanwhile, trader Y takes an equivalent long position in euro futures - which have a standard notional of €125,000 - requiring 16 contracts to match X’s exposure. At the end of 60 days, the spot rate rises to 1.1500 USD/EUR. Trader X realises the entire gain at maturity:

Payoff_forward = (Sₜ – Fₜ) × Notional

Payoff_forward = (1.1500 – 1.0800) × €2,000,000

Payoff_forward = 0.0700 × €2,000,000 = $140,000

Trader Y ultimately realises the same total gain - $140,000 - but through a series of daily mark-to-market adjustments over the life of the futures contract. Each day, the change in futures price generates either a margin call or a margin credit. Over the 60-day period, these daily gains and losses accumulate to the same $140,000 profit.

The key difference is timing and risk: trader X is exposed to the full counterparty risk until maturity, while trader Y settles gains and losses daily, reducing credit exposure through the clearinghouse’s margin system. Therein, we can see why futures are often preferred when liquidity, transparency, and credit risk mitigation are priorities - whereas forwards are more appropriate for bespoke exposures that require custom terms.

Determination of forward prices

Forward contracts on foreign currencies are priced using the same no‑arbitrage principles we have applied to other assets. In this case, each currency carries its own risk‑free interest rate, and the connection between the spot exchange rate and the forward rate reflects the difference between these rates. If the forward rate does not align with interest‑rate differentials, arbitrageurs can borrow in one currency, convert at the spot rate, invest in the other currency, and lock in a reverse transaction via a forward, earning a risk‑free profit. Such trading ensures that the forward rate moves to eliminate any arbitrage.

To see how this works, imagine two risk‑free interest rates, one for domestic currency (rₙ) and one for foreign currency (rₓ), both expressed as continuously compounded per annum. Let S₀ be today’s spot rate (the amount of domestic currency per unit of foreign currency) and let F₀ be the forward rate agreed for delivery in T years. If the forward rate is set too high, an investor can borrow 1 unit of the foreign currency at rate rₓ for T years, convert it into S₀ units of domestic currency, and invest at rate rₙ. Simultaneously, the investor enters a forward contract to sell the proceeds of this domestic investment back into one unit of foreign currency at rate F₀. By maturity, the domestic investment has grown to S₀ e^rₙT, which under the forward yields:

(S₀ erₙT)/(F₀ ) 

units of foreign currency. The loan repayment is e^rₓT units of foreign currency. Therefore, a risk‑free profit arises if:

(S₀ erₙT)/(F₀ ) > e^rₓT

A mirror‑image arbitrage exists if the forward rate is too low: an investor borrows S₀ units of domestic currency at rate rₙ, converts to 1 unit of foreign currency, invests at rate rₓ, and enters a forward to buy back the domestic currency. No‑arbitrage requires these two profits to vanish, leading to the covered interest rate parity formula:

F₀ = S₀ · e ^{(rₙ – rₓ) T}

This relationship shows that the forward rate rises when the domestic interest rate exceeds the foreign rate and falls when the reverse holds. It is the cornerstone of currency forward pricing.

This is clearer within an example. Suppose a nine‑month forward to buy USD is negotiated when S₀ = 1.10 GBP/USD, rₙ = 3% p.a., rₓ = 1% p.a., and T = 0.75 years. Plugging into the formula gives:

F₀ = S₀ · e ^{(rₙ – rₓ) T}

F₀ = 1.10 × e ^{{(0.03 – 0.01) × 0.75}} ≈

1.10 × e^0.015 ≈ 1.1166 GBP/USD.

Any quoted rate above or below this level would allow arbitrageurs to borrow‑convert‑invest‑forward or its reverse, locking in a risk‑free profit and restoring the forward rate to S₀ · e ^{{(rₙ – rₓ) T}}.

To simplify practical calculations, traders often use a discrete, one-year version of the interest rate parity relationship. This version expresses the no-arbitrage forward rate F as a function of the spot rate S₀​ and the respective one-year interest rates r_n​ (domestic) and r_x​ (foreign), both expressed as decimals. It captures the same principle: the forward rate must prevent arbitrage opportunities arising from borrowing, converting, investing, and reversing the transaction at maturity.

Suppose today’s spot rate is S₀ domestic currency per unit of foreign currency, and the one‑year interest rates are rₙ for the domestic currency and rₓ for the foreign, both expressed as decimals. The no‑arbitrage forward rate F for one year ahead must satisfy the relationship:

F = S₀ · ((1 + rₙ))/((1 + rₓ))

To see why, imagine that the quoted forward rate exceeds S₀ · ((1 + rₙ))/((1 + rₓ)). An arbitrageur could borrow one unit of foreign currency at rate rₓ for one year, convert this into S₀ units of domestic currency at the spot rate, and invest it at rate rₙ for one year. At the same time, the arbitrageur enters a forward contract to buy one unit of foreign currency in one year at the rate F. When the year is up, the domestic investment has grown to S₀ · (1 + rₙ), which is paid under the forward to receive one unit of foreign currency. The arbitrageur then repays (1 + rₓ) on the original foreign loan and pockets the difference. If F is higher than S₀ · ((1 + rₙ))/((1 + rₓ)), this difference is positive, allowing a risk‑free profit. A mirror‑image sequence applies if F is too low, so competition drives the forward rate back to the stated formula.

Suppose the spot rate is S₀ = 1.10 GBP/USD, the one‑year GBP rate is rₙ = 3% per annum, and the one‑year USD rate is rₓ = 1% per annum, then:

F = S₀ · ((1 + rₙ))/((1 + rₓ))

F = 1.10 ·  ≈ 1.1228 GBP/USD.

Should the market quote any other forward rate, the borrow‑convert‑invest‑forward strategy would lock in a risk‑free gain, and arbitrageurs would trade it away, restoring F to S₀ · ((1 + rₙ))/((1 + rₓ)).

Forward Rate Agreements

Not all forwards are created equal, nor do they all serve the same purpose. Some forwards are structurally different, and one such contract is that of the Forward Rate Agreement. Forward Rate Agreements (FRAs) are bespoke over‑the‑counter contracts that enable institutions and corporations to lock in an implied future interest rate today, without ever exchanging the underlying principal. By agreeing on a notional amount (L), a fixed rate R_K​, and a future period of length t years (for instance, three months corresponds to t = 0.25), both parties commit to settle the difference between the agreed fixed rate and the market’s floating reference rate R_F​ (such as SOFR or LIBOR) observed at the start of that period. Although the full notional L remains untouched, the net interest differential:

Δ = (R_K − R_F) t L

is calculated at the period’s end. If R_K​ exceeds RF​, the fixed‑rate receiver collects Δ; if R_F​ is higher, the fixed‑rate payer collects ∣Δ∣. Because settlement ordinarily occurs at the period’s end, the payment Δ is discounted back to the start of the period using the prevailing zero‑rate (z) over the time T from today until settlement. The present value of the FRA is therefore:

PV_FRA = Δ e−^zT

At inception, R_K​ is set equal to the market’s forward rate R_F^fwd​ for the same period, ensuring that PV₀ = 0. As market expectations evolve, forward rates shift and the FRA’s value becomes positive or negative, reflecting gains or losses for the fixed‑rate receiver or payer.

Consider a practical example: a trader hedges a three‑month borrowing of £100 million beginning two years hence by entering an FRA with R_K=3%. At the contract’s start, the two‑year forward SOFR is indeed 3%, so the FRA is initially worthless (PV₀ = 0). Two years later, if three‑month SOFR has risen to 3.5%, the un‑discounted payoff is:

Δ = (0.03 − 0.035) × 0.25 × 100,000,000 = −£125,000

meaning the fixed‑rate receiver owes £125 000. Discounting this amount back over the three‑month period at z = 3.5% yields approximately −£124,891. One net cash settlement thus replaces otherwise uncertain floating‑rate interest payments, providing effective protection against adverse rate moves.

In this way, FRAs offer a simple yet powerful tool for managing future interest‑rate exposure. By converting variable obligations into fixed commitments (or vice versa) without exchanging principal, they deliver budgeting certainty and balance‑sheet stability in environments where rate volatility can pose significant financial risk.

Conclusion

In conclusion, forward contracts provide a versatile and powerful framework for managing future financial exposures. By fixing prices or rates today, parties can hedge against unfavourable movements in currencies, interest rates, or other assets, trading uncertainty for predictability. The pricing of forwards is firmly anchored in the principles of no-arbitrage and interest rate parity, ensuring alignment with spot markets and prevailing interest rates. While forwards carry counterparty risk due to their over-the-counter nature, their customisability makes them ideal for bespoke needs not met by standardised futures contracts. Additionally, specialised forward contracts like Forward Rate Agreements enable effective management of interest rate risk without exchanging principal. Together, these instruments form a foundational part of modern financial markets, balancing risk and opportunity in an ever-changing economic environment.

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