Forward Exchange, FX Swaps and Interest Parity

Introduction

Foreign exchange markets allow institutions to exchange currencies immediately or at a future date. A spot transaction settles near the present market date, whereas a forward transaction fixes today the exchange rate for an exchange occurring in the future. An FX swap combines a near-date exchange with a reverse exchange at a later date. These instruments are central to international funding, treasury management, hedging, market-making and foreign investment.

The pricing of forwards and swaps is governed principally by covered interest parity (CIP). CIP links the spot exchange rate, the forward exchange rate and the interest rates available in the two currencies. When markets are liquid and transaction costs are low, a forward rate that differs materially from its parity value creates an arbitrage opportunity. In practice, however, balance-sheet costs, credit risk, collateral requirements, regulation and market liquidity influence observed prices.

Learning objectives

By the end of this chapter, the reader should be able to:

1. Explain the economic purpose and structure of outright forwards and FX swaps.
2. Distinguish direct and indirect exchange-rate quotations.
3. Calculate theoretical forward rates using covered interest parity.
4. Interpret forward points and price an outright forward.
5. Calculate the economics of an FX swap and distinguish swap points from the outright forward rate.
6. Identify the steps in a covered interest arbitrage.
7. Apply forwards and swaps to funding and hedging decisions.
8. Evaluate practical limitations of interest-parity pricing.

1. Exchange-rate quotations and market conventions

Suppose EUR/USD is quoted as 1.0850. This means that one euro costs 1.0850 US dollars. The euro is the base currency and the US dollar is the terms currency. A quotation of USD/JPY 150.00 means that one US dollar costs 150 Japanese yen.

The spot rate is denoted by S, expressed as units of domestic or terms currency per unit of foreign or base currency. Thus, if the investor’s domestic currency is USD and the foreign currency is EUR, S = USD ext{/}EUR. A forward rate is denoted by F_T, where T is the maturity date or tenor.

Market participants must state clearly:

• currency pair and quotation direction;
• value dates and settlement conventions;
• notional amount and which currency is the base amount;
• business-day adjustments and holidays;
• interest-rate basis, such as 360 or 365 days;
• whether rates are simple, continuously compounded or compounded periodically.

A quotation can be inverted. If EUR/USD is 1.0850, then USD/EUR is approximately 0.9217, calculated as 1 ÷ 1.0850. Forward points must also be inverted consistently; they cannot simply be transferred from one quotation direction to the other.

2. Outright FX forwards

An outright forward is an agreement to exchange a specified amount of one currency for another at a specified future date and exchange rate. No principal exchange normally occurs at trade inception. At maturity, the parties exchange the agreed currencies, regardless of the prevailing spot rate.

A corporation expecting to pay EUR 10 million in three months may buy euros forward against dollars. The forward removes uncertainty about the dollar cost. An exporter expecting euro receipts may sell euros forward to lock in the domestic-currency value.

The forward normally has zero value at inception when it is transacted at the prevailing market forward rate, ignoring credit, funding and transaction-cost effects. After inception, its value changes as spot rates, interest rates, credit spreads and remaining maturity change.

Forward points

The forward points are commonly defined as:

where P_T is the forward-point adjustment in quotation units, F_T is the outright forward rate and S is the spot rate. Therefore:

If EUR/USD spot is 1.0850 and three-month forward points are +0.0024, the outright forward rate is 1.0874. If points are quoted as 24 points, where one point is 0.0001, the same result follows: 1.0850 + 24 × 0.0001 = 1.0874.

A positive forward premium does not necessarily mean that the euro is expected to appreciate. It usually reflects the interest-rate differential and, in practice, also a cross-currency basis and liquidity effects.

3. Covered interest parity

3.1 Economic derivation

Consider an investor who has domestic currency for a period and wishes to obtain a foreign-currency return while eliminating exchange-rate risk. The investor can either:

1. invest directly in the domestic currency; or
2. convert into foreign currency at spot, invest in the foreign currency, and sell the future foreign proceeds forward.

No-arbitrage requires the two covered strategies to produce the same domestic-currency amount. Under simple interest, with domestic interest rate i_d, foreign interest rate i_f and year fraction τ, the parity relationship for a quotation of domestic currency per unit of foreign currency is:

Here, S and F_T have units of domestic currency per foreign currency; i_d and i_f are annualized rates expressed as decimals; and τ is the accrual fraction, such as 90/360. Both sides therefore have the same exchange-rate units.

The formula assumes that borrowing and lending rates are available at the stated rates, the two currencies can be exchanged freely, principal amounts are certain, settlement dates match, and transaction costs, credit risk, collateral effects and capital constraints are negligible. These assumptions describe a theoretical benchmark rather than every real market transaction.

With continuously compounded rates, the corresponding expression is:

where r_d and r_f are continuously compounded domestic and foreign rates. With annual effective rates, the simple-interest formula should not be used; the relevant accumulation factors must be substituted.

3.2 Interpretation

If the domestic interest rate exceeds the foreign interest rate, the domestic currency normally trades at a forward discount in a domestic-per-foreign quotation: the forward rate is higher than spot. The higher domestic return must be offset by a higher future domestic-currency price of the foreign currency.

If the foreign interest rate exceeds the domestic rate, the foreign currency normally trades at a forward discount and F_T < S. This is a pricing relationship, not a reliable forecast of future spot rates.

The forward premium or discount can be annualized approximately as:

This approximation is useful for short maturities. It is not identical to the interest differential when compounding and basis effects are material.

4. Worked example: pricing an outright forward

Assume:

• spot EUR/USD = 1.0800;
• three-month USD interest rate = 5.20% per annum;
• three-month EUR interest rate = 3.20% per annum;
• simple interest and a 90/360 year fraction, so τ = 0.25.

Using CIP:

The accumulation factors are 1.0130 and 1.0080. Hence:

The forward points are therefore approximately:

or about 53.6 EUR/USD points. A firm buying EUR 10 million forward will pay approximately USD 10.8536 million at maturity, assuming the quoted amount is EUR 10 million and the forward rate is 1.08536 USD per EUR.

The result is economically consistent: USD interest is higher than EUR interest, so EUR is more expensive in forward USD terms than in spot terms.

5. FX swaps

An FX swap is a simultaneous agreement to:

• exchange two currencies on a near date, usually spot or tomorrow/next; and
• reverse the exchange on a later date at a pre-agreed rate.

The near leg and far leg have the same currency notionals in the usual structure, although the exchange rates differ. An FX swap is therefore not simply an outright forward. It is a temporary currency exchange, often used to obtain short-term funding or manage currency liquidity.

For example, a bank needing dollars for one month may sell euros and receive dollars in the near leg, while agreeing to buy back euros and return dollars in the far leg. The transaction resembles secured borrowing and lending, although legal documentation, collateral and counterparty exposures determine the exact risk profile.

Swap points

The swap points are:

When the near leg is spot, this becomes F_T − S. The far-leg outright rate is obtained by adding the points to the near-leg rate, subject to quotation convention. Dealers quote bid and offer swap points because the institution buys one currency on one leg and sells it on the other.

An FX swap quote may therefore appear as:

The swap points represent the relative financing cost of the two currencies over the swap period. They are not a separate prediction of the future spot rate.

FX swap versus currency swap

An FX swap generally has a short or medium maturity and exchanges principal at the near and far dates, with no periodic interest coupons. A cross-currency swap normally has longer maturity, may exchange principal at inception and maturity, and includes periodic interest payments in the two currencies. The instruments have related economic logic but different documentation, cash-flow patterns and risk management requirements.

6. Worked example: an FX swap funding decision

A treasury desk owns EUR 50 million and needs USD for 30 days. It can enter a EUR/USD FX swap with:

• near-leg rate: 1.0800 USD/EUR;
• 30-day swap points: +0.0018;
• far-leg rate: 1.0818 USD/EUR.

At the near date, the desk sells EUR 50 million and receives:

At the far date, it buys back EUR 50 million and pays:

The gross dollar financing cost is USD 90,000 for 30 days, before fees, credit adjustments and collateral effects. The implied simple annualized cost relative to the dollars received is approximately:

This calculation is an interpretation of the swap price, not necessarily the desk’s all-in funding cost. The desk must also consider the opportunity cost of the euros, bid-offer spreads, margin and the credit valuation of the counterparty.

7. Covered interest arbitrage

A covered interest arbitrage exists when the market forward rate differs sufficiently from the parity-implied rate to cover transaction costs and risks. The standard procedure is:

1. calculate the theoretical forward rate;
2. compare it with the executable market forward rate;
3. identify the currency that is overpriced or underpriced forward;
4. borrow in one currency;
5. convert at spot;
6. invest in the other currency;
7. cover the future exchange with a forward;
8. repay the borrowing and retain any residual profit.

Illustrative arbitrage

Suppose spot EUR/USD is 1.0800, the three-month USD rate is 5.20%, the EUR rate is 3.20%, and the theoretical forward is 1.08536. If an executable market forward is 1.0900, euros are expensive in the forward market relative to this simplified parity benchmark.

A trader can borrow euros, convert them into dollars at spot, invest the dollars, and sell the future dollars to buy euros forward. The exact notional should be selected so that the future euro proceeds repay the euro borrowing. If the forward market is sufficiently mispriced, the locked-in dollar proceeds exceed the dollar repayment.

In a professional setting, the apparent profit must be recalculated using bid and offer prices, actual deposit and borrowing rates, settlement conventions, credit limits, collateral, capital charges, taxes and the cost of executing all legs. Many apparent arbitrage opportunities disappear after these adjustments.

8. Hedging and funding applications

Importer hedge

An importer with a known foreign-currency payable faces uncertainty in the domestic-currency cost. Buying the foreign currency forward fixes the exchange rate. The hedge sacrifices potential gains if the foreign currency depreciates, but it protects the budget from appreciation.

Exporter hedge

An exporter expecting foreign-currency receipts can sell the foreign currency forward. The domestic value becomes predictable, supporting cash-flow planning and debt-service management.

Foreign investment

An investor purchasing a foreign bond has both asset-return risk and currency risk. Selling the expected foreign-currency proceeds forward can reduce exchange-rate volatility, although the hedge ratio may need adjustment when coupons, market values or cash flows change.

Treasury funding

An institution can use an FX swap to transform temporary currency liquidity. It may borrow dollars against euros, or euros against dollars, without establishing a long-term open currency position. The choice depends on relative funding rates, liquidity, collateral and balance-sheet capacity.

Hedge effectiveness

A forward hedge may not eliminate all risk. Maturity mismatch, uncertain transaction size, timing changes, credit events and differences between the hedged exposure and the forward notional create basis or operational risk. A treasury policy should specify hedge objectives, permitted instruments, hedge ratios, documentation, valuation procedures and escalation limits.

9. Practical limitations of interest parity

CIP is a no-arbitrage benchmark, not an unconditional law. Deviations may arise from:

• bid-offer spreads and brokerage costs;
• different borrowing and lending rates;
• counterparty credit and settlement risk;
• collateral and margin requirements;
• regulatory capital and liquidity charges;
• balance-sheet scarcity, especially at reporting dates;
• restrictions on capital movement;
• differences in tax, legal and settlement systems;
• cross-currency basis, reflecting the relative scarcity of funding in a currency;
• differences between secured and unsecured interest rates.

The modern pricing practice often replaces simple unsecured interest rates with appropriate collateralized discount curves and a separately observed cross-currency basis. Accordingly, the dealer’s forward price may be represented conceptually as the parity value adjusted for basis, funding, credit and transaction costs.

A forward’s market value is also distinct from its forward rate. The rate is the contractual exchange rate for a new transaction. The value is the present value of the difference between the contractual rate and the current market replacement rate, discounted consistently in both currencies. A transaction can have a zero initial value but become a significant asset or liability later.

10. Risk, governance and regulation

FX forwards and swaps create counterparty exposure, market exposure, settlement exposure and operational risk. Institutions commonly manage these through master agreements, netting, collateral arrangements, settlement controls, independent valuation and limits by counterparty, currency and maturity.

The treasury function should distinguish:

• market risk: changes in spot rates, interest rates and basis;
• credit risk: counterparty failure before or at settlement;
• liquidity risk: inability to obtain or roll funding;
• legal risk: unenforceable netting or unclear documentation;
• model risk: incorrect curves, conventions or quotation direction;
• conduct risk: unsuitable hedging, misleading pricing or inadequate disclosure.

Transactions should be confirmed promptly, valued independently and reconciled against confirmations and settlement instructions. Where the instruments qualify as accounting hedges, formal documentation and effectiveness testing may be required under the applicable accounting framework.

Technology supports automated curve construction, real-time valuation, collateral management, confirmation matching and limit monitoring. AI may assist with anomaly detection or liquidity forecasting, but it does not remove the need for explainable models, data controls, human approval and governance. A model that learns from historical prices can fail during a regime change, market closure or extreme liquidity event.

11. Illustrative case: multinational funding and hedging

Background

This fictional case concerns Meridian Components, a UK-based manufacturer that will receive EUR 20 million in 90 days from a German customer. It also has a USD 15 million payment due in 60 days to a US supplier. The firm’s functional currency is GBP.

Problem

Meridian faces two distinct exposures. The euro receivable may lose sterling value if the euro depreciates. The dollar payable may become more expensive in sterling if the dollar appreciates. The company also has surplus euros for part of the period but needs dollars before the euro receipt arrives.

Analysis

The receivable and payable should not automatically be treated as one net exposure because their currencies, amounts and dates differ. The treasury team obtains executable forward prices, estimates cash-flow dates, reviews credit lines and compares a direct USD borrowing with an FX swap using available euros.

Approach and solution

Meridian sells the expected EUR 20 million receipt forward against GBP for the 90-day date. This stabilizes the sterling value of the euro cash flow. It buys USD 15 million forward against GBP for the 60-day payment, thereby fixing the sterling cost. For interim liquidity, it uses a 30-day EUR/USD FX swap only if it has euros available and the swap’s all-in cost is lower than alternative secured funding.

The team documents the hedge ratios, confirms the settlement dates, monitors forecast changes and tests the effect of a 5% adverse currency movement. It also establishes a fallback plan if the customer’s payment is delayed, because a forward remains binding even when the underlying cash flow changes.

Outcome

The company achieves predictable sterling cash flows and avoids converting a temporary liquidity need into a long-term speculative currency position. It does not eliminate all risk: timing mismatch, counterparty exposure, forward replacement cost and funding liquidity remain.

Learning points

The case demonstrates that instrument selection follows exposure analysis. An outright forward is appropriate for a known future cash flow; an FX swap is appropriate for temporary currency funding; and CIP is a pricing benchmark rather than a substitute for cash-flow, credit and liquidity analysis.

Best-practice pricing and decision framework

A professional workflow is:

1. define the exposure, currency pair, notional and settlement dates;
2. establish the quotation direction and day-count convention;
3. obtain independent spot, interest-rate and basis inputs;
4. calculate the parity benchmark;
5. compare benchmark and executable bid-offer prices;
6. include funding, collateral, credit, capital and operational costs;
7. select the instrument according to the exposure rather than the market view;
8. document the hedge purpose and authority;
9. confirm, settle and independently revalue the transaction;
10. monitor residual risks and close or roll the hedge under approved limits.

Chapter Summary

An outright forward fixes an exchange rate today for a future currency exchange. An FX swap combines a near exchange with a reverse far-date exchange and is widely used for short-term currency funding and liquidity management. Forward points equal the difference between the forward and near-leg rates, subject to quotation convention.

Covered interest parity states that the forward rate is determined by the spot rate adjusted for the relative accumulation factors of the two currencies. Under simple interest, F_T = S × (1 + i_dτ) ÷ (1 + i_fτ). The relationship is a no-arbitrage benchmark based on matched borrowing, lending, spot conversion and forward cover. In practice, basis, transaction costs, credit, collateral, regulation and balance-sheet constraints affect executable prices.

Forwards are particularly useful for hedging known foreign-currency receipts and payments. FX swaps are particularly useful for temporary currency funding. Effective professional application requires more than formulaic pricing: it requires correct conventions, independent valuation, risk limits, documentation, settlement controls and analysis of residual liquidity and counterparty risks.

Key Terms

Forward exchange: Agreement to exchange currencies on a future date at a rate fixed today.

FX swap: Near-date currency exchange combined with a reverse exchange at a later date.

Spot rate: Current exchange rate for standard near-date settlement.

Forward rate: Contractual exchange rate for a future currency exchange.

Forward points: Difference between the forward rate and the spot or near-leg rate.

Outright forward: A standalone forward currency transaction without a near leg.

Covered interest parity: No-arbitrage relationship connecting spot, forward and interest rates.

Base currency: First currency in a currency quotation.

Terms currency: Currency in which the base currency is priced.

Direct quotation: Exchange rate stated in domestic currency per unit of foreign currency.

Cross-currency basis: Market adjustment reflecting deviations from the simplest interest-parity benchmark.

Value date: Date on which currency settlement occurs.

Year fraction: Accrual period expressed according to a specified day-count convention.

Hedge ratio: Proportion of an exposure covered by a hedging instrument.

Settlement risk: Risk that one party pays but does not receive the expected currency.

Counterparty risk: Risk that the other party fails to perform.

Funding liquidity risk: Risk of being unable to obtain currency funding when needed.

Mark-to-market value: Current replacement value of an existing contract.

Bid-offer spread: Difference between executable buying and selling prices.

Covered interest arbitrage: Matched borrowing, investing, spot conversion and forward cover intended to exploit mispricing.

Review Questions

Short Answer Questions

1. What is the difference between an outright FX forward and an FX swap?
2. Define forward points and explain how they relate to the outright forward rate.
3. State the simple-interest covered interest parity formula and define its variables.
4. Why does a higher domestic interest rate generally produce a higher forward rate in a domestic-per-foreign quotation?
5. Identify two practical reasons why observed forward prices may differ from a simplified CIP calculation.

Long Answer Questions

1. Explain the economic derivation of covered interest parity using domestic investment and covered foreign investment strategies.
2. Discuss the uses of FX swaps in bank treasury and corporate funding management.
3. Explain the distinction between the forward rate and the market value of a forward contract.
4. Evaluate the risks involved in using forwards to hedge forecast foreign-currency cash flows.
5. Describe a complete professional process for pricing, approving, confirming and monitoring an FX forward.

Analytical / Application Questions

1. Spot EUR/USD is 1.1000, the 180-day USD rate is 6.00% and the EUR rate is 4.00%, using simple interest and a 360-day basis. Calculate the theoretical forward rate and explain the direction of the forward points.
2. A firm will receive EUR 8 million in 120 days and reports in USD. Design a hedge using an outright forward and explain the principal residual risks.
3. A bank can obtain dollars through an FX swap or unsecured borrowing. Identify the cash flows and variables that should be compared before selecting the cheaper funding method.

Multiple Choice Questions with Answers

Question 1

Under a domestic-per-foreign quotation, which formula represents simple-interest covered interest parity?

A. F_T = S × (1 + i_fτ) ÷ (1 + i_dτ)

B. F_T = S × (1 + i_dτ) ÷ (1 + i_fτ)

C. F_T = S + i_d + i_f + τ

D. F_T = S × (i_d − i_f) × τ

Correct Answer: B. F_T = S × (1 + i_dτ) ÷ (1 + i_fτ)

Question 2

Spot EUR/USD is 1.0800 and forward points are +0.0024. What is the outright forward rate?

A. 1.0776

B. 1.0800

C. 1.0824

D. 1.1040

Correct Answer: C. 1.0824

Question 3

What is the principal purpose of an FX swap?

A. To obtain temporary currency funding or liquidity

B. To create an equity ownership position

C. To guarantee a future spot rate forecast

D. To eliminate all counterparty risk

Correct Answer: A. To obtain temporary currency funding or liquidity

Question 4

If the domestic interest rate is higher than the foreign interest rate, what normally occurs in a domestic-per-foreign quotation under CIP?

A. The forward rate is below spot

B. The forward rate equals zero

C. The forward rate is above spot

D. The spot rate must immediately rise

Correct Answer: C. The forward rate is above spot

Question 5

A 30-day FX swap exchanges EUR 50 million at 1.0800 and reverses at 1.0818. How many USD are received on the near leg?

A. USD 50.000 million

B. USD 52.000 million

C. USD 54.000 million

D. USD 54.090 million

Correct Answer: C. USD 54.000 million

Question 6

Which strategy is consistent with covered interest arbitrage when the forward price of euros is too high relative to parity?

A. Borrow euros, buy dollars spot, invest dollars and sell dollars forward for euros

B. Borrow dollars, buy euros spot and leave the future exchange uncovered

C. Buy euros forward and borrow euros at maturity

D. Invest in both currencies without using a forward

Correct Answer: A. Borrow euros, buy dollars spot, invest dollars and sell dollars forward for euros

Question 7

Which item is not normally a limitation of a simplified CIP calculation?

A. Bid-offer spreads

B. Collateral and capital costs

C. Counterparty credit risk

D. The definition of the base currency being irrelevant

Correct Answer: D. The definition of the base currency being irrelevant

Question 8

An importer with a known foreign-currency payable will commonly hedge by:

A. Selling the foreign currency forward

B. Buying the foreign currency forward

C. Selling the domestic currency spot and leaving the exposure open

D. Borrowing only in the foreign currency after the payable date

Correct Answer: B. Buying the foreign currency forward

Question 9

If EUR/USD spot is 1.0850 and the forward rate is 1.0874, the forward points are:

A. −0.0024

B. 0.0000

C. +0.0014

D. +0.0024

Correct Answer: D. +0.0024

Question 10

Which statement best distinguishes an FX swap from an outright forward?

A. An FX swap has a near leg and a far reverse leg

B. An FX swap never involves exchange of principal

C. An outright forward always has two currency exchanges

D. An outright forward is used only for speculation

Correct Answer: A. An FX swap has a near leg and a far reverse leg