For OIS, and for loans and bonds whose floating rate is set by compounding in arrears, the interest is calculated from TONA. When an OIS net amount is settled or interest compounded in arrears is paid, the time at which the Bank of Japan publishes TONA decides when the amount to be paid and received can be fixed.

What kind of rate TONA is

TONA is a benchmark rate derived from one-day borrowing and lending between financial institutions. Consider a hypothetical example in which Bank A borrows 10 billion yen from Bank B for one day at 0.5% a year. Prorating on a 365-day year, the interest Bank A pays on top of the principal on the next business day is 136,986 yen (rounded down to the nearest yen).

The market in which financial institutions even out their day-to-day short-term surpluses and shortages of funds is called the call market1. Trades in this market without collateral are called uncollateralized call trades. Among them, trades agreed today, funded today and repaid on the next business day are called overnight (O/N) trades2.

Because TONA is a rate for a single day, it is not a rate for a period such as three or six months. To use it for a period, you build up the daily TONA over that period (see "How TONA is used" below). A rate quoted for a period longer than one day, such as one week or three months, is called a term rate, and a term rate whose value is set at the start of the period is said to be fixed in advance.

In December 2016, the Study Group on Risk-Free Reference Rates selected TONA as the Japanese yen risk-free rate (RFR)3. The Study Group concluded that, although the trades carry the counterparty's credit risk because they are uncollateralized, that risk is limited because the lending lasts only one day, so the rate is close to risk-free4.

The name varies from source to source. TONA stands for Tokyo Overnight Average Rate5, and some sources write TONAR6. The Bank of Japan's statistics call it the uncollateralized call O/N rate7. Its monetary policy statements call it the uncollateralized overnight call rate8. The Bank of Japan sets its guideline for money market operations by stating the level around which it will encourage this rate to remain8.

How the Bank of Japan calculates and publishes TONA

The Bank of Japan calculates and publishes TONA every business day from trade data it receives from money market brokers. The process runs as follows.

  1. Financial institutions agree uncollateralized O/N call trades through money market brokers.
  2. The money market brokers (Ueda Yagi Tanshi, Central Tanshi and Tokyo Tanshi) provide the rate and amount of each trade to the Bank of Japan9.
  3. The Bank of Japan calculates the average of the rates weighted by the volume at each rate, and publishes a preliminary figure the same day.
  4. The Bank of Japan publishes the final figure on the next business day.

The publication times are as follows10.

Figure Publication time
Preliminary Around 5:15 p.m. on the day (around 6:15 p.m. on the last day of a month, except the last day of the year)
Final Around 10:00 a.m. on the next business day

Figure 1 puts the O/N trades on one business day (day T) and the publication of TONA for that day in time order.

Day TO/N trades are agreed and funds aredeliveredDay T5:15 p.m.Preliminary TONA for day T ispublishedNextbusiness dayTrades mature.Funds are repaidNextbusiness dayFinal TONA for day T is published at10:00 a.m.
Figure 1The order of O/N trades and TONA publication
Figure description

On day T, financial institutions agree O/N trades and funds are delivered. The Bank of Japan publishes the preliminary figure for TONA for day T, in principle, at around 5:15 p.m. on day T (around 6:15 p.m. on the last day of a month, except the last day of the year). The trades mature on the next business day, when the borrower repays the funds. The final figure for TONA for day T is published on that same next business day, at around 10:00 a.m. The final figure is the one used for the floating rate of an OIS. The times in the figure are publication times and do not show the time of day at which the trades mature.

Only trades arranged by money market brokers go into the calculation. Trades that financial institutions agree directly with each other without a broker (direct dealing) are left out. When selecting the RFR, the Study Group concluded that this framework could stay as it was, because trades arranged by money market brokers alone had a reasonable volume11.

A rate multiplied by its volume is called the rate-volume product. The weighted average is found by adding up the products for each rate and dividing by the total volume. The result is given to three decimal places (rounded at the fourth decimal place)9. Consider a hypothetical example in which trades on one day were agreed at three rates.

Rate (%) Volume (billion yen) Product (rate × volume; % × billion yen)
0.470 200 94
0.480 500 240
0.490 300 147
Total 1,000 481

Dividing the total product of 481 by the total volume of 1,000 gives 0.481, so TONA for the day is 0.481%. More was traded at 0.490% (300 billion yen) than at 0.470% (200 billion yen), so the result is higher than the simple average of the three rates (0.480%). Along with the weighted average, the Bank of Japan also publishes the day's highest and lowest rates and the O/N trading volume12.

How TONA is used

To use TONA for a period, the daily TONA over the interest period is compounded at the end of the period to set the rate. This method is called compounding in arrears, and the rate is fixed only after TONA for the last day of the period has been published. The formula, the treatment of holidays and numerical examples are covered in Compounding in Arrears.

A typical use is the OIS (overnight index swap). A Japanese yen OIS is an interest rate swap that exchanges a fixed rate for a floating rate calculated by compounding TONA over a set period13. In the Study Group's April 2018 document, the reference index for the floating rate of a yen OIS is the final figure for TONA14. How OIS work and their cash flows are covered in Overnight Index Swaps (OIS).

Publication of yen LIBOR (London Interbank Offered Rate) ended at the end of December 202115. Following a public consultation in July 2019, TONA compounded in arrears was selected as one of the candidates to replace yen LIBOR16. With TONA compounded in arrears, the rate is fixed just before the interest payment date. TORF (Tokyo Term Risk Free Rate) and TIBOR (Tokyo Interbank Offered Rate) are fixed in advance, at the start of the period, so the amount of interest becomes known at a different time17.

Notes

  1. Bank of Japan, "コール市場" (The call market), 教えて！にちぎん (in Japanese). It lists banks, trust banks, shinkin banks, investment trusts, securities companies, insurance companies and the money market brokers that act as intermediaries among the participants. Checked on September 25, 2026. ↩

  2. Bank of Japan Financial Markets Department, "「コール市場関連統計」の解説" (Explanation of call market statistics, in Japanese), "１．公表内容" (Published data), page 1. It defines the uncollateralized O/N rate as "無担保コール市場における、当日約定、当日資金受渡し、翌営業日を期日とする条件で成立した取引のレート" (the rate on trades in the uncollateralized call market done on terms of same-day agreement, same-day delivery of funds and maturity on the next business day; our translation). ↩

  3. Study Group on Risk-Free Reference Rates, "日本円のリスク・フリー・レートの特定に関する報告書" (Report on the Identification of a Japanese Yen Risk-Free Rate, December 2016, in Japanese), "Ⅰ．概要" (Overview), page 1. An English version is available: "Report on the Identification of a Japanese Yen Risk-Free Rate", "1. Summary", page 1. ↩

  4. The same document, "Ⅱ－２．市中協議を踏まえた検討事項に対する本勉強会の整理" (The Study Group's conclusions on the issues considered after the public consultation), item ②, page 4. In the English version, "2-2. Conclusion of the Study Group", item (2), pages 4–5. ↩

  5. JBA TIBOR Administration, "金利指標改革を踏まえた全銀協TIBORの現状および今後の展望（2026年６月）詳細説明資料" (The current state and outlook of JBA TIBOR in light of benchmark reform, June 2026, detailed explanatory material, in Japanese), note *1 to the table on page 9. It says "TONAは、Tokyo Overnight Average Rateの略" (TONA is short for Tokyo Overnight Average Rate; our translation). ↩

  6. Financial Conduct Authority, "About LIBOR transition", the table "RFRs recommended as alternatives to LIBOR". The row for Japan reads "Tokyo Overnight Average Rate (TONAR)". Checked on September 25, 2026. ↩

  7. Bank of Japan Financial Markets Department, "「コール市場関連統計」の解説" (in Japanese), "データ始期" (Start of data) on page 1 and "（２）無担保コールＯ／Ｎ物取引の出来高" ((2) Volume of uncollateralized O/N call trades) on page 2. ↩

  8. Bank of Japan, "金融市場調節方針の変更について" (Change in the Guideline for Money Market Operations, June 16, 2026, in Japanese), item 1, page 1. An English version is available: "Change in the Guideline for Money Market Operations", item 1, page 1. ↩ ↩2

  9. Bank of Japan Financial Markets Department, "「コール市場関連統計」の解説" (in Japanese), "２．コールレートの算出方法" (How call rates are calculated), page 2. The names of the money market brokers are taken from the document's list of "情報提供会社" (data providers). ↩ ↩2

  10. The same document, the table in "３．公表方法" (Publication method), page 2. ↩

  11. Study Group on Risk-Free Reference Rates, "日本円のリスク・フリー・レートの特定に関する報告書" (December 2016, in Japanese), "Ⅱ－２．市中協議を踏まえた検討事項に対する本勉強会の整理" (The Study Group's conclusions on the issues considered after the public consultation), item ①, page 3. In the English version, "2-2. Conclusion of the Study Group", item (1), page 4. ↩

  12. Bank of Japan Financial Markets Department, "「コール市場関連統計」の解説" (in Japanese), "１．公表内容" (Published data), pages 1–2. ↩

  13. Study Group on Risk-Free Reference Rates, "日本円ＯＩＳ（Overnight Index Swap）─取引の概要と活用事例─" (Yen OIS: overview of transactions and examples of use, April 2018, in Japanese), "２．OIS とは何か" (What is an OIS?), page 3. ↩

  14. The same document, "参照指数" (Reference index) under "基本的な取引方式" (Basic trading terms), page 5. ↩ ↩2

  15. 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. An English version is available: "Review of JPY LIBOR Transition and Future Initiatives" (Bank of Japan Review 2022-E-4, May 2022), "Introduction", page 1. ↩

  16. "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, in Japanese), the main text on page 3. It says that the first public consultation, conducted by the Cross-Industry Committee on Japanese Yen Interest Rate Benchmarks in July 2019, showed that three candidates, TORF, TONA compounded in arrears and TIBOR, were "選好された" (preferred; our translation). The English version (Bank of Japan Review 2022-E-4) says the same on page 3. ↩

  17. "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, in Japanese), Chart 2, page 3. Under "金利決定のタイミング" (timing of rate fixing; our translation), it gives "前決め" (fixed in advance) for TORF and TIBOR and "後決め（金利支払日の直前）" (fixed in arrears, just before the interest payment date; our translation) for TONA compounded in arrears. Chart 2 on page 3 of the English version (Bank of Japan Review 2022-E-4) shows the same. ↩

  18. Study Group on Risk-Free Reference Rates, "日本円ＯＩＳ（Overnight Index Swap）─取引の概要と活用事例─" (Yen OIS: overview of transactions and examples of use, April 2018, in Japanese), "例２" (Example 2), page 6. ↩