How Swaps Work

A corporate treasurer who wants to fix the interest rate on a loan, or a financial institution that needs foreign-currency funding, needs to understand how a swap contract is set up.

What the contract sets

A swap is one kind of derivative. In the Bank of Japan's derivatives statistics, a swap is a contract to exchange cash flows worked out by an agreed calculation method, usually in several rounds during a set period. It is a product category alongside forward contracts (forwards) and options¹. How derivatives work in general is covered in What Is a Derivative?.

Take a fictional example of the most basic kind of interest rate swap, between Company A and Bank F. A swap contract mainly sets the following four things about the cash flows (payments of money) to be exchanged.

The parties choose how often payments are made, such as daily, monthly, every three months, or once a year². An interest rate swap does not exchange the notional amount itself, but some trades, such as cross-currency swaps, do exchange an amount equal to the notional³.

This is a contract in which two parties, Company A and Bank F, each pay the other interest. Company A pays Bank F an amount calculated at the fixed rate, and on the same payment date Bank F pays Company A an amount calculated at the floating rate. Both amounts are calculated from the same notional amount set in the contract; only the calculation method differs. The notional amount itself is not exchanged between the two parties.

Payments on each payment date

From Company A's side, the amount it pays is set when the trade is made. On each of the four payment dates, from 1 year to 4 years after the start, Company A pays 100 million yen (5 billion yen × 2%). The amount it receives is set for each payment date by the floating rate for the calculation period ending on that date. This example uses the floating rate at the start of each calculation period⁴. In this form, only the amount received after 1 year is known when the trade is made. The amounts received after 2 to 4 years are not yet known.

Figure description

Payments of Company A, which pays the fixed side of a swap with a notional amount of 5 billion yen and a fixed rate of 2% a year. On the payment dates after 1, 2, 3 and 4 years, Company A pays 100 million yen of fixed-rate interest each time. On the same dates, it receives an amount calculated at the floating rate. The amount after 1 year is set by the floating rate at the time of the trade, but the amounts after 2 to 4 years are not yet set. The length of the receiving arrows is only a guide and does not show an amount.

When both parties owe each other amounts on the same payment date, they may net them so that one party pays only the difference, instead of both paying in full⁵. For example, if the floating rate for the first year is 2.4%, Bank F owes 120 million yen. Netting this against the 100 million yen Company A owes means that Bank F only pays Company A 20 million yen.

Main types: what is exchanged

A swap's name depends on the kind of payments exchanged⁶. The typical ones exchange different kinds of interest in the same currency, or interest and other payments in different currencies⁷. There are also swaps linked to equities or commodities⁸.

Among interest rate swaps, the exchange of a fixed rate for a floating rate is the most typical form⁷. The names of interest rate swaps also include the OIS (overnight index swap)⁹.

A cross-currency swap exchanges future interest and principal between different currencies, such as receiving US dollar interest and paying yen interest. A swap that exchanges only the interest, without the principal, is called a coupon swap⁷. In the typical US dollar/yen cross-currency swap between banks, the parties exchange principal and also exchange US dollar floating interest for yen floating interest¹⁰. The similarly named FX swap is a different trade.

In a commodity swap, one party receives the value of a set quantity of a commodity at the market price on each payment date, and pays a fixed amount¹¹.

Other trades also have "swap" in their names. Some are linked to share prices, and others to the creditworthiness of a company or country. One example of the latter is the credit default swap (CDS)¹².

Viewing a swap as a bundle of forwards

The payments of a swap can often be viewed as a bundle of forward contracts, one for each payment date¹³. A forward contract is a trade to exchange an asset on a set future date at a price agreed in advance¹⁴. How forward contracts work is covered in Forwards and Futures.

Take a fictional commodity swap. On each payment date, one party receives the value of 10,000 units of a commodity at the market price on that date, and pays 50 million yen, calculated at a fixed price of 5,000 yen per unit. If the price on a payment date is 5,500 yen per unit, this party receives a net 5 million yen. If the price is 4,500 yen, it pays 5 million yen. These amounts are the same as for a forward contract to buy 10,000 units at 5,000 yen per unit on that payment date, settled by paying only the difference without delivering the commodity. With four payment dates, the swap is four forward contracts with different delivery dates, bundled together at the same fixed price.

The value of a forward contract can be calculated by a known method, so splitting a swap into forward contracts also gives the value of the swap¹³.

Deep diveValuing a commodity swap with forward prices

Consider a commodity swap on $N$ units in which, on the $i$-th payment date, one party receives the market price $S_i$ on that date and pays a fixed price $X$. Let $F_i$ be today's price of a forward contract for delivery on the $i$-th payment date, and $d(0, i)$ the discount factor to that date. Receiving the market price $S_i$ on the $i$-th payment date has the same value today as receiving $F_i$ on the same date. So the value of a swap with $M$ payment dates is given by the following formula¹⁵.

$$V = N \sum_{i=1}^{M} d(0, i)\,(F_i - X)$$

The fixed price $X$ is normally set so that this $V$ is zero. If the forward price $F_i$ differs across payment dates, the difference from $X$ is positive on some dates and negative on others, and the discounted total is zero.

Value at the start

In many swaps, the fixed rate or price is set so that, at the start of the trade, the present values of what each party will receive are equal¹⁶. This means that, apart from fees and similar costs, neither party pays anything to enter the trade. In the commodity swap in the previous section, assume that the fixed price of 5,000 yen per unit was set to meet this condition. However, when terms are changed to suit what one party asks for, the swap may not be worth zero at the start, and one party pays the other the difference¹⁶.

Once the trade has started, movements in interest rates or prices move the value of the swap away from zero, so it can become positive or negative. Because the two parties simply exchange payments, the value to one party is the value to the other with the sign reversed¹⁷.

What swaps are used for

Swaps spread among financial institutions as a way to manage gains and losses from future changes in interest rates, and companies also use them in managing their finances¹⁸. A company that borrows at a floating rate can add an interest rate swap in which it pays fixed and receives floating, which turns the loan into the equivalent of a fixed-rate loan. A company that borrows at a fixed rate can enter the opposite swap to get the equivalent of a floating-rate loan¹⁹.

Fixing interest payments is a form of hedging against the cost of higher rates. Suppose Company A has borrowed 5 billion yen at a floating rate and has entered the swap above. Assume the loan's floating rate is the same as the swap's floating rate.

In a year when the floating rate is 3%, the interest on the loan is 150 million yen. Through the swap, Company A receives 150 million yen of floating-rate interest and pays 100 million yen of fixed-rate interest, so it receives a net 50 million yen. Subtracting this 50 million yen from the 150 million yen of loan interest leaves Company A with a cost of 100 million yen (2% a year).

In a year when the floating rate is 1%, the loan interest is 50 million yen. Through the swap, Company A receives 50 million yen and pays 100 million yen, so it pays a net 50 million yen. Adding this 50 million yen to the 50 million yen of loan interest again gives a cost of 100 million yen, so Company A does not benefit from the fall in rates²⁰. In both years, Bank F's swap payments are Company A's amounts with the sign reversed.

Cross-currency swaps are used to turn foreign-currency payments into yen payments. For example, buying a bond denominated in US dollars means receiving the interest and the principal at redemption in US dollars. This creates currency risk, the risk from changes in the rate at which US dollars and yen are exchanged. Entering a cross-currency swap at the same time can create the same effect as investing in a yen-denominated bond¹⁸. Cross-currency swaps are also one of the main ways that financial institutions outside the United States obtain US dollar funding²¹.

A swap can also be entered without combining it with the payments on a loan or an asset. One such use is speculation, betting on whether the floating rate will rise or fall compared with current expectations²².

Counterparty risk

The Bank of Japan's derivatives statistics cover OTC derivatives (trades not made through an exchange), and swaps are one of their categories¹. Cross-currency swaps are also bilateral trades that do not go through an exchange²³. In a swap agreed directly between the parties like this, the party for which the swap has a positive value may be unable to receive that value if the other party defaults²⁴. However, the notional amount used to calculate the payments does not directly show the size of this loss²⁴.

Notes

1. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」の解説" (Explanation of the Regular Derivatives Market Statistics, in Japanese; March 2020), "ロ）スワップ" (Swaps) under "2）商品別" (By product) in "（2）計数の区分" (Classification of figures). The opening of the same explanation states that the statistics cover outstanding amounts in the OTC derivatives market. The categories under "By product" are forwards, swaps, options and other products. An English outline is also available: "Outline of 'Regular Derivatives Market Statistics'". ↩ ↩²

2. Society of Actuaries, "Interest Rate Swaps" (FM-25-17), page 4. It calls the payment dates settlement dates and the time between them the settlement period. ↩

3. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」の解説" (in Japanese; March 2020), "1）想定元本" (Notional amount). It states "金利関連取引など多くのデリバティブ取引では想定元本自体は受け渡しされませんが、外為関連取引のように想定元本額相当の受け渡しが発生する場合もあります" (in many derivative trades, such as interest rate trades, the notional amount itself is not exchanged, but in some cases, such as foreign exchange trades, an amount equal to the notional amount is exchanged; our translation). ↩

4. Society of Actuaries, "Interest Rate Swaps", Example 1 on page 5. The interest paid at the end of year one is set by the rate at the start of year one. Martin Haugh's "Forwards, Swaps, Futures and Options", section 2.1 on page 4, also takes each period's floating rate as the rate at the start of the period. ↩

5. Society of Actuaries, "Interest Rate Swaps", page 4. It gives an example in which two payments at the same time are netted and only the difference is paid (the net swap payment). ↩

6. Japan Exchange Group, "スワップ（用語集）" (Swap, glossary, in Japanese). ↩

7. Central Council for Financial Services Information, "4-1 スワップ取引とは（やさしいデリバティブ）" (What is a swap, Easy Derivatives, in Japanese), "スワップの種類" (Types of swaps). ↩ ↩² ↩³

8. Martin Haugh, "Forwards, Swaps, Futures and Options" (lecture notes for IEOR E4706 at Columbia University, 2016), section "2 Swaps" on page 4. It says "Other types of swaps include equity and commodity swaps". ↩

9. Takashi Kawakami, "ヘッジ取引におけるデリバティブ信用評価調整の影響についての考察" (A study of the effect of credit valuation adjustments on hedging trades, in Japanese), Bank of Japan Institute for Monetary and Economic Studies, Kinyu Kenkyu (April 2018), "1. はじめに" (Introduction), page 120. It gives the Japanese name "翌日物金利スワップ" together with "Overnight Index Swap: OIS". ↩

10. Bank of Japan, "（日銀レビュー）店頭デリバティブ取引データからみた通貨スワップ市場：感染症拡大の影響とその後の回復を中心に" (Bank of Japan Review: The cross-currency swap market seen through OTC derivatives data, focusing on the impact of the spread of COVID-19 and the subsequent recovery, in Japanese; May 2021), "通貨スワップ取引の概要" (Overview of cross-currency swap trades), page 2. It names the dollar/yen basis swap as the typical interbank trade. ↩

11. Martin Haugh, "Forwards, Swaps, Futures and Options", Example 3 on page 5. ↩

12. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」の解説" (in Japanese; March 2020), "ホ）クレジット" (Credit) under "1）リスク・ファクター別" (By risk factor) in "（2）計数の区分" (Classification of figures), and "ホ）クレジット" (Credit) under "5）その他の区分" (Other classifications). ↩

13. Martin Haugh, "Forwards, Swaps, Futures and Options", section "2.3 Pricing Swaps" on page 5. It says "the cash-flow stream of a swap can often be considered as a stream of forward contracts". ↩ ↩²

14. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」の解説" (in Japanese; March 2020), "イ）フォワード" (Forwards) under "2）商品別" (By product). ↩

15. Martin Haugh, "Forwards, Swaps, Futures and Options", the formula in Example 3 on page 5. The symbols are the same as in the source. ↩

16. Society of Actuaries, "Interest Rate Swaps", page 5. The fixed rate of an interest rate swap is set so that the present values of both sides' payments are equal, and in customized swaps one party may pay a difference (premium). For the fixed price of a commodity swap, see Martin Haugh's "Forwards, Swaps, Futures and Options", Example 3 on page 5. ↩ ↩²

17. Society of Actuaries, "Interest Rate Swaps", section "6 Market Value" on page 15. ↩

18. Central Council for Financial Services Information, "4-1 スワップ取引とは（やさしいデリバティブ）" (in Japanese), "通貨スワップ" (Cross-currency swaps), "スワップ取引は金利変動リスクの管理に向いている" (Swaps are suited to managing interest rate risk) and "金利変動リスクの管理と「金利スワップ」" (Managing interest rate risk and interest rate swaps). ↩ ↩²

19. Society of Actuaries, "Interest Rate Swaps", pages 3–4. It gives examples of using a swap to turn a floating-rate loan into a fixed-rate one and a fixed-rate loan into a floating-rate one. ↩

20. Central Council for Financial Services Information, "4-2 金利スワップの仕組み（やさしいデリバティブ）" (How interest rate swaps work, Easy Derivatives, in Japanese), the example of borrowing at a floating rate. It states "予想に反して金利が下落した場合には、そのメリットが受けられなくなる" (if rates fall contrary to expectations, the borrower cannot receive that benefit; our translation). ↩

21. Bank of Japan, "（日銀レビュー）店頭デリバティブ取引データからみた通貨スワップ市場：感染症拡大の影響とその後の回復を中心に" (Bank of Japan Review: The cross-currency swap market seen through OTC derivatives data, focusing on the impact of the spread of COVID-19 and the subsequent recovery, in Japanese; May 2021), the summary on page 1. It states "通貨スワップ取引は、非米系金融機関にとって、米ドル資金の主要な調達手段の一つ" (for non-US financial institutions, cross-currency swaps are one of the main means of obtaining US dollar funds; our translation). ↩

22. Society of Actuaries, "Interest Rate Swaps", page 4. It lists speculation as one reason for entering an interest rate swap without an underlying loan. ↩

23. Bank of Japan, "（日銀レビュー）店頭デリバティブ取引データからみた通貨スワップ市場：感染症拡大の影響とその後の回復を中心に" (Bank of Japan Review: The cross-currency swap market seen through OTC derivatives data, focusing on the impact of the spread of COVID-19 and the subsequent recovery, in Japanese; May 2021), the summary on page 1. ↩

24. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」の解説" (in Japanese; March 2020), "（2）想定元本、正の市場価値と信用リスク・エクスポージャー" (Notional amounts, positive market values and credit exposure). ↩ ↩²