Cross-Currency Swaps

Cross-currency swaps are used when a bank raises funds in a foreign currency, and when an institutional investor such as a life insurance company reduces the exchange rate risk of its foreign currency assets.

Exchanging principal and floating rates: the structure and the example's terms

A cross-currency swap is a trade that exchanges funds in different currencies over an agreed period, usually one year or longer¹. In the representative interbank USD/JPY trade, the parties exchange principal and also exchange the US dollar 3-month reference rate for the yen 3-month reference rate plus the cross-currency basis¹. An early example is the trade the World Bank entered into with IBM in 1981. The World Bank describes it as "the world's first formal currency swap agreement."² The general structure of swaps, and how cross-currency swaps differ from interest rate swaps and other types, are covered in How Swaps Work.

From here on, this page covers the form in which the parties exchange principal at the start and at maturity, and exchange floating rates in the two currencies during the term and at maturity. This form is called a cross-currency basis swap (the Bank of Japan working paper calls it a basis swap)³⁴. Some cross-currency swaps exchange fixed rates, and a form that exchanges only interest, without exchanging principal, is called a coupon swap⁵.

Consider a hypothetical example in which Bank L in Japan enters into a cross-currency swap with N Securities, which holds dollars. Bank L pays yen and receives dollars, and N Securities does the opposite.

This example uses 6-month floating rates. The value of the cross-currency basis is set at the market level when the trade is agreed⁶.

The reference rate for the floating rates used to be LIBOR⁷. It was announced that the main tenors of US dollar LIBOR would stop being published at the end of June 2023⁸. In August 2021, the Cross-Industry Committee on Japanese Yen Interest Rate Benchmarks, for which the Bank of Japan serves as secretariat, published a statement on the transition policy for quotes in the cross-currency swap market (RFR First)⁸.

Payments and receipts from the start to maturity

Bank L pays 15 billion yen and receives USD 100 million at the start, and pays USD 100 million and receives 15 billion yen at maturity. Because the principal exchange at maturity also uses the spot exchange rate at the start, the principal amounts exchanged back do not change even if the spot exchange rate moves during the term⁹⁴. On each payment date every six months during the term, Bank L receives yen interest and pays dollar interest.

Figure description

The payments and receipts of Bank L, which pays yen and receives dollars, in a 2-year cross-currency swap with a dollar principal of USD 100 million and a yen principal of 15 billion yen. At the start, Bank L receives USD 100 million and pays 15 billion yen. After 6 months, 1 year, 18 months, and 2 years, it receives yen interest calculated at the yen floating rate plus the cross-currency basis, and pays dollar interest calculated at the dollar floating rate. The interest amounts depend on the floating rates, so they are not known when the trade is agreed. After 2 years, together with the last interest, Bank L receives the same 15 billion yen as at the start and pays USD 100 million. The principal and interest after 2 years are combined into one arrow for yen and one for dollars, labeled "JPY 15bn" (15 billion yen) and "USD 100mn" (USD 100 million) with "+ interest". The arrow lengths are only a guide and do not show the size of the amounts. The payments and receipts of N Securities are in the opposite direction to Bank L's at every point in time.

Each interest payment is calculated by multiplying the principal in each currency by that currency's interest rate. If the yen floating rate for a 6-month period is 0.50% a year and the dollar floating rate is 4.00% a year, the payments and receipts on that payment date are as follows¹⁰.

Which side carries the cross-currency basis, and its sign

In a USD/JPY cross-currency swap, the cross-currency basis is added to the yen floating rate¹⁶. For other currency pairs against the dollar as well, the market standard in 2010 was to add no spread to the dollar floating rate and to add it to the floating rate of the other currency¹¹. Because the dollar side is a rate with no spread, the cross-currency basis is a signed value seen from the side of the currency other than the dollar.

A negative cross-currency basis means that demand for dollar funds is relatively strong¹. With the −0.20% in the example, the yen interest Bank L receives is 22.5 million yen, which is 15 million yen less than the 37.5 million yen (15 billion yen × 0.50% × 0.5) it would receive with a cross-currency basis of zero. For the party that pays yen and receives dollars, this 15 million yen is an extra cost of obtaining dollars. Expressed as a positive number, this extra cost is called the dollar funding premium. In this example, the size of the negative cross-currency basis, 0.20%, corresponds to it¹². Conversely, a positive cross-currency basis means that demand for yen funds is relatively strong, and the yen interest Bank L receives increases⁶.

Why the cross-currency basis is not zero, and the background to the periods when its negative value widened, are covered in Covered Interest Parity and FX Forward Points.

When the exchange rate and the cross-currency basis move

Because the principal at maturity is exchanged at the spot exchange rate at the start, a profit or loss arises on the principal exchange if the spot exchange rate at maturity differs from the one at the start. At maturity, Bank L pays USD 100 million and receives 15 billion yen. Measured at the spot exchange rate at maturity, the results are as follows.

If the yen is stronger and the dollar weaker at maturity, Bank L, which received dollars, gains, and if the yen is weaker and the dollar stronger, it loses. N Securities' profit or loss has the opposite sign to Bank L's in every case.

The value of the cross-currency basis is set when the trade is agreed and does not change until maturity. Suppose that after the trade, the market cross-currency basis for the same term falls to −0.40%. Bank L's trade has a cross-currency basis of −0.20%, so it receives 15 million yen (15 billion yen × 0.20% × 0.5) more per six months than a trade agreed now, and the value of Bank L's side rises. Conversely, if the market cross-currency basis rises to 0.00%, Bank L receives 15 million yen less per six months than a trade agreed now, and the value of its side falls.

What cross-currency swaps are used for

Cross-currency swaps are one of the main ways that financial institutions outside the United States obtain dollar funding¹³. In 2007, the main purposes were as follows¹⁴.

• Managing foreign currency funding
• Speculation based on views on interest rates
• Arbitrage with other products
• Covering other financial products
• Raising foreign currency for hedged investment in foreign bonds and for direct investment
• Hedging when issuing bonds denominated in foreign currencies

Institutional investors such as life insurance companies also use cross-currency swaps to hedge the currency risk of their foreign currency assets¹⁵.

To check the hedging effect, take an example in which Bank L uses the USD 100 million it received to make a 2-year dollar floating rate loan. During the term, Bank L uses the dollar interest it receives on the loan to pay the dollar interest on the cross-currency swap. At maturity, it passes the USD 100 million repaid on the loan to N Securities under the cross-currency swap and receives 15 billion yen.

With a spot exchange rate of 140 yen at maturity, the cross-currency swap on its own gains 1 billion yen, and with 160 yen it loses 1 billion yen, but combined with the loan the result is 15 billion yen in both cases. Bank L receives in yen at maturity the same amount it paid at the start, 15 billion yen. In return, while it avoids the loss from a stronger yen reducing the yen value of the loan, it also gives up the gain from a weaker yen increasing it.

Issuers of bonds denominated in foreign currencies can use the same structure. When a foreign entity issues a yen-denominated bond (a Samurai bond), combining a yen interest rate swap with a USD/JPY cross-currency swap reduces its interest rate and exchange rate risks¹⁶.

Cross-currency swaps and FX swaps both exchange funds in different currencies for a set period, and they have similar economic effects. Converting the floating rate of a cross-currency swap into a fixed rate with an interest rate swap makes it comparable with an FX swap of the same term, so arbitrage is thought to work between the two markets¹⁷¹⁸¹⁹.

Cross-currency swaps that adjust the principal during the term

A cross-currency swap that adjusts the principal during the term is called a mark-to-market cross-currency swap. In this form, the principal in the currency that carries no spread is reset at the spot exchange rate at the start of each calculation period. The difference between the principal for the previous period and for the next period is paid or received between the two parties at that time. The principal in the other currency stays the same until maturity. In USD/JPY, the dollar side carries no spread, so the dollar principal is usually the one adjusted²².

Suppose the trade in the example is changed to the form that adjusts the principal. The yen principal stays at 15 billion yen, and the dollar principal is reset at the spot exchange rate after six months.

The dollar principal for the next period is 15 billion yen divided by the spot exchange rate at that time²³. If the spot exchange rate moves to 160 yen, the dollar principal that Bank L returns at the end of the next period falls from USD 100 million to USD 93.75 million, and Bank L pays the difference of USD 6.25 million to N Securities. The dollar interest for the next period is also calculated on the new principal of USD 93.75 million. This trade can be viewed as a series of one-period cross-currency swaps with the same principal, and the net of the principal exchange at the end of the previous period and the exchange at the start of the next period equals the payment or receipt that adjusts the principal²².

Converting USD 6.25 million into yen at 160 yen gives 1 billion yen, the same amount as the 1 billion yen loss that arises in the form without principal adjustment when the spot exchange rate at maturity is 160 yen. In a cross-currency swap that does not adjust the principal, the profit or loss from changes in the exchange rate builds up until the principal exchange at maturity. In the form that adjusts the principal, the amount up to that point is paid or received each period.

Counterparties and market structure

Cross-currency swaps are bilateral trades that do not go through an exchange²⁴. Because they exchange principal, in the form that does not adjust the principal, movements in the exchange rate increase the profit or loss on the principal exchange at maturity, and the value of the trade moves far from zero. In a bilateral OTC derivative, the party for which the trade has a positive value may be unable to receive the amount equal to that value if the other party defaults²⁵.

In the international survey of turnover in April 2019, the yen had the largest turnover among cross-currency swaps against the dollar, and trades in Japan made up about a quarter of USD/JPY cross-currency swap turnover, second only to the United Kingdom. In Japan, financial institutions account for most of the trading²⁶. In the May 2021 Bank of Japan Review, which looked at reported data on OTC derivatives trades in Japan by type of institution, major banks and similar institutions were the main takers of dollars, and foreign banks and securities companies were the main providers of dollars²⁷.

When conditions for raising dollars deteriorated sharply in the spring of 2020, the major financial institutions that act as intermediaries kept trading while making each trade smaller and spreading trades across more counterparties²⁸.

Notes

1. Bank of Japan Financial Markets Department, "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" (The cross-currency swap market seen through OTC derivatives data, focusing on the impact of the spread of COVID-19 and the subsequent recovery) (Bank of Japan Review, May 2021, in Japanese), "通貨スワップ取引の概要" (Overview of cross-currency swap trades, page 2). It explains the reference rates of the USD/JPY basis swap and how to read the sign of the cross-currency basis. ↩ ↩² ↩³ ↩⁴

2. World Bank, "The World Bank Treasury | IBRD • IDA: 70 Years Connecting Capital Markets to Development", Chapter 4. ↩

3. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (Arbitrage relationship and price discovery between cross-currency swaps and FX swaps, in Japanese) (Bank of Japan Working Paper Series No.07-J-13, November 2007), "2-2. ベーシス・スワップの基本的なフレームワーク" (2-2. Basic framework of basis swaps), page 4. As of 2007, the paper calls this form a "ベーシス・スワップ" (basis swap; our translation) and says that 3- and 6-month LIBOR is common for the floating rates. The summary and "1-1. 問題意識・目的" (1-1. Issues and objectives, page 1) also describe the same form. ↩

4. Bank of Japan, "グローバルな為替スワップ市場の動向について" (Bank of Japan Review, July 2016, in Japanese), note 1 (page 7). It explains trades that make the principal exchanged at the end the same as at the start. An English version is available: "Recent Trends in Cross-currency Basis" (Bank of Japan Review 16-E-7, September 2016). The note and page numbers refer to the Japanese version. ↩ ↩²

5. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), note 1 (page 1). ↩

6. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), "2-2. ベーシス・スワップの基本的なフレームワーク" (2-2. Basic framework of basis swaps) and note 7 (page 4). It describes α as "実際に市場で値付けされているベーシス・スワップの価格" (the price of the basis swap actually quoted in the market; our translation) and states "ドル円では、円LIBORに付加されるのが市場慣例" (in USD/JPY, the market convention is to add it to yen LIBOR; our translation). Note 7 says that a positive (negative) α indicates relatively strong demand for yen (dollar) funds. ↩ ↩² ↩³

7. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), note 5 (page 7). It states "これまで参照金利は Libor が利用されてきたが、金利指標改革を受けて、今後は徐々にリスク・フリー・レートへの移行が進むと考えられる" (Libor has so far been used as the reference rate, but following the reform of interest rate benchmarks, a gradual transition to risk-free rates is expected; our translation). ↩

8. Bank of Japan Financial Markets Department and Financial System and Bank Examination Department, and Financial Services Agency Strategy Development and Management Bureau and Supervision Bureau, "円LIBOR移行対応の振り返りと今後の取り組み" (Bank of Japan Review 2022-J-8, May 2022, in Japanese), "はじめに" (Introduction, page 1), the explanation of the establishment of the Cross-Industry Committee (page 2), and Chart 3 (page 3). An English version is available: "Review of JPY LIBOR Transition and Future Initiatives" (Bank of Japan Review 2022-E-4, May 2022). The page and chart numbers refer to the Japanese version. ↩ ↩²

9. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), note 6 (page 4). It states "元本は、期中での為替直物レートの変化の影響を受けない。エンド時の交換レートにも、スタート時の為替直物レートが適用される" (the principal is not affected by changes in the spot exchange rate during the term. The spot exchange rate at the start is also applied as the exchange rate at the end; our translation). ↩

10. For simplicity, six months is treated as 0.5 years. In actual trades, the length of each period is counted using the day count convention of each currency. ↩

11. Masaaki Fujii, Yasufumi Shimada, and Akihiko Takahashi, "A Note on Construction of Multiple Swap Curves with and without Collateral" (CIRJE-F-630, revised January 2010), Section 3.5 (page 14). ↩

12. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), "はじめに" (Introduction, page 1), "通貨スワップ取引の概要" (Overview of cross-currency swap trades, page 2), and note 2 to Chart 17 (page 6). The source's term is "ドル調達プレミアム" (dollar funding premium; our translation). ↩

13. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), the summary (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). ↩

14. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), "2-2. ベーシス・スワップの基本的なフレームワーク" (2-2. Basic framework of basis swaps, pages 4–5) and "1. ベーシス・スワップの主な利用目的" (1. Main purposes of using basis swaps) in the appendix (page 23). ↩

15. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), note 7 (page 7). It says that institutional investors such as life insurance companies use cross-currency swaps and FX swaps to hedge their investments in foreign currency assets. ↩

16. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), the appendix (page 24) and Appendix Chart 2. ↩

17. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), "1-4. 無裁定関係と価格発見力" (1-4. No-arbitrage relationship and price discovery, page 3) and "2-1. ベーシス・スワップと為替スワップの共通点と相違点" (2-1. Similarities and differences between basis swaps and FX swaps, page 4). ↩

18. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), "2-4. ベーシス・スワップの固定金利化と裁定機会" (2-4. Converting basis swaps into fixed rates and arbitrage opportunities, page 6). ↩

19. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), note 4 (page 7). It states "両者は同様の経済効果を持つ取引として、裁定が働くと考えられる" (as trades with similar economic effects, arbitrage is thought to work between the two; our translation). ↩

20. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), the explanation of item ③ in the appendix (page 23). As examples, it names "仕組み債や輸入企業のフラット為替取引" (structured notes and flat-rate FX contracts for importers; our translation). The note number after "仕組み債" (structured notes) in the original is omitted. ↩

21. Yasuaki Amatatsu and Naohiko Baba, "通貨スワップと為替スワップの裁定関係と価格発見力" (in Japanese), "2-3. 為替スワップの基本的なフレームワーク" (2-3. Basic framework of FX swaps, page 5). ↩

22. Masaaki Fujii, Yasufumi Shimada, and Akihiko Takahashi, the same paper, Section 3.5 (page 14) and Section 2 (page 2). The paper abbreviates it as MtMCCS. ↩ ↩²

23. Amounts are rounded down to the nearest dollar. 15 billion yen ÷ 140 yen is USD 107,142,857.14. ↩

24. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), the summary (page 1). ↩

25. Bank of Japan Financial Markets Department, "「外国為替およびデリバティブに関する中央銀行サーベイ」の解説" (Explanation of the "Central Bank Survey of Foreign Exchange and Derivatives Market Activity", in Japanese), "（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" ((2) Notional amounts, positive market values, and credit exposure). ↩

26. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), "通貨スワップ取引の概要" (Overview of cross-currency swap trades) and "本邦通貨スワップ市場の特徴" (Features of the Japanese cross-currency swap market) (page 2), and Charts 2, 4, and 5. The figures come from the BIS Triennial Central Bank Survey of Foreign Exchange and Derivatives Market Activity (April 2019), and Japan's share is 24.3% in Chart 4. ↩

27. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), page 4 and Charts 9 and 10. ↩

28. Bank of Japan Financial Markets Department, "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, May 2021, in Japanese), the summary (page 1) and "2020 年春前後の取引動向" (Trading around the spring of 2020, pages 4–5). ↩