Interest rate futures are used both by companies that want to fix the rate on future borrowing today and by financial institutions that read the level of a future rate from futures prices.

Prices expressed as "100 minus the rate"

Interest rate futures are futures contracts that trade, today, the short-term interest rate for a set period in the future. The main products all cover a three-month period. Osaka Exchange's 3-Month TONA Futures cover the rate obtained by compounding TONA (Tokyo Overnight Average Rate) daily over three months and annualizing the result. The Bank of Japan publishes TONA. The price is 100 minus that rate1. TONA is the rate on funds that financial institutions borrow from each other without collateral today and repay the next day2. How TONA is calculated and published is covered on the TONA page.

Consider a hypothetical example in which the interest rate futures price for a contract month is 99.000. The three-month rate that the contract month covers is then being traded at 1.000% a year. A price of 98.500 means 1.500% a year, and 99.500 means 0.500% a year. When the three-month period ends and the actual rate is known, that rate sets the final settlement price, and the difference from the traded price is the final profit or loss of the buyer and the seller of the futures.

The three-month period covered is called the reference period. For Osaka Exchange's 3-Month TONA Futures, it runs from the third Wednesday of March, June, September, or December to the day before the third Wednesday three months later. A contract month is named after the month in which its reference period starts. For example, the September contract covers the rate from the third Wednesday of September to the day before the third Wednesday of December. The last trading day is, in principle, the last day of the reference period (the day before the third Wednesday three months later, moved back to the previous business day if it falls on a holiday)3.

Rate moves and the seller's and buyer's profit or loss

Because the price is expressed as 100 minus the rate, the futures price falls when the rate rises and rises when the rate falls. Tokyo Financial Exchange's Three-month TONA Futures also quote the price as 100 minus the rate, in the same way as bonds2. Interest rate futures follow the practice of placing orders on the value of 100 minus the rate, and this way of quoting is called the IMM index method4. IMM (International Monetary Market) is the name of the market that CME (Chicago Mercantile Exchange) in the United States opened in 19725.

The size of a gain or loss depends on the amount per 0.01% (1bp) of the rate. For Osaka Exchange's 3-Month TONA Futures, the trading value of one contract is the price multiplied by 250,000 yen. The multiplier is set so that 1 point of price (1% of rate) equals 250,000 yen, the interest on a face value of 100 million yen borrowed for three months (0.25 years)4. A price move of 0.01 therefore changes the profit or loss on one contract by 2,500 yen, and Tokyo Financial Exchange's Three-month TONA Futures also set the value of 1bp at 2,500 yen2. For one contract traded at 99.000, the profit or loss at expiry is as follows.

Rate for the period (% a year) Final settlement price Seller's profit or loss (yen) Buyer's profit or loss (yen)
0.500 99.500 −125,000 125,000
1.000 99.000 0 0
1.500 98.500 125,000 −125,000

If the rate rises 0.5% (50bp) above the 1.000% at the time of the trade, the seller gains 50 × 2,500 yen, or 125,000 yen, and the buyer loses the same amount. If the rate falls 0.5%, the result is reversed. Whatever the rate, the seller's and the buyer's profits or losses add up to 0.

−1.5−1.0−0.50.0+0.5+1.0+1.599Profit/loss (points)Final settlement price (points)ProfitLossBreakeven 99
Figure 1Profit or loss at expiry for the seller of interest rate futures at 99.000
Figure description

This chart shows, in price points, the profit or loss at expiry for the side that sold one interest rate futures contract at 99.000. The horizontal axis is the final settlement price and the vertical axis is the profit or loss, which is a straight line that falls by the same amount as the price rises. It is 0 at a price of 99.000. Below that price (a rate above 1.000%) the seller has a profit, and above it (a lower rate) the seller has a loss. At a price of 98.000 (a rate of 2.000%) the seller gains 1 point, and at 100.000 (a rate of 0%) the seller loses 1 point. For 3-Month TONA Futures, 1 point equals 250,000 yen. The seller of futures gains when the rate rises.

TONA and SOFR futures and the discontinued ones

In Japan, three-month interest rate futures based on TONA are listed on both Osaka Exchange and Tokyo Financial Exchange67. CME in the United States lists three-month interest rate futures based on SOFR (Secured Overnight Financing Rate)8. SOFR is a rate that measures the cost of overnight borrowing secured by US Treasury securities, and the Federal Reserve Bank of New York (New York Fed) administers it9. The Alternative Reference Rates Committee (ARRC), which has led the transition of US dollar benchmark rates, mentioned the strong growth in SOFR futures trading in an announcement in May 202210.

The product names follow each exchange's own spelling of "month" (Osaka Exchange writes "3-Month" and Tokyo Financial Exchange writes "Three-month").

Product Exchange Underlying rate Reference period
3-Month TONA Futures Osaka Exchange TONA compounded daily over three months (annualized on an actual/365 basis) Three months from the third Wednesday of March, June, September, or December
Three-month TONA Futures Tokyo Financial Exchange TONA compounded daily over three months (annualized on an actual/365 basis) Three months from the third Wednesday of March, June, September, or December
Three-Month SOFR Futures CME SOFR compounded daily over three months (annualized on an actual/360 basis) From the March, June, September, or December IMM date (a quarterly Wednesday) to the next IMM date

The day count conventions and periods in the table can be checked in each exchange's materials and in a filing that CME submitted to the US Commodity Futures Trading Commission (CFTC)632811.

There were also interest rate futures on a three-month interbank rate rather than on compounded overnight rates. Tokyo Financial Exchange's three-month Euroyen futures covered three-month Euroyen TIBOR (Tokyo Interbank Offered Rate)1213, but trading stopped at 3:30 p.m. on June 28, 202414. Euroyen TIBOR itself ceased publication at the end of December 202415.

In the United States, CME's Three-Month Eurodollar Futures covered three-month US dollar LIBOR (London Interbank Offered Rate)16. In February 2021, CME filed rule amendments with the CFTC under which, when LIBOR ended, the remaining open interest in Eurodollar futures would be converted into the corresponding SOFR futures17.

Final settlement on the compounded rate

Tokyo Financial Exchange's Three-month TONA Futures are settled in cash at final settlement. The final settlement price is calculated in the following steps2.

  1. For each business day in the reference period, multiply TONA by the number of days it applies to and divide by 365 to get that day's rate (when a holiday intervenes, the same TONA applies to a day count that includes the holiday).
  2. Multiply together all the values of 1 plus the rates from step 1, then subtract 1 to get the compounded rate for the period.
  3. Multiply the result of step 2 by "365 ÷ the number of calendar days in the period" to annualize it.
  4. Express it as a percentage, round it to three decimal places (rounding at the fourth), and subtract it from 100 to get the final settlement price.

Consider a hypothetical example in which the reference period is 91 days, every day is a business day, and TONA is 1.000% every day. The compounded rate for the period is about 0.2496%, which annualizes to about 1.0012%. Rounding at the fourth decimal place gives 1.001%, so the final settlement price is 98.999. Because the daily rates are compounded, the annual rate comes out slightly higher than the simple rate of 1.000%, even though every daily rate is 1.000%. Setting the rate at the end of the period by compounding each day's overnight rate is called compounding in arrears.

Another feature of interest rate futures is that gains and losses build up without waiting for expiry. For exchange-traded futures, the central counterparty revalues open positions and settles the resulting gains and losses every day (mark-to-market)18. When a customer trades through a firm (a financial instruments business operator), the daily valuation gains and losses are added to or subtracted from the calculation of the margin deposited with that firm. If losses bring the margin below the required amount, the customer deposits more, and if there are gains, the customer can withdraw them within certain limits19. At final settlement, the customer and the firm exchange the profit or loss based on the difference between the final settlement price and the traded price, minus any gains withdrawn along the way. The customer's total profit or loss therefore comes to this difference20.

Fixing the rate on future borrowing

Interest rate futures are used for hedging against changes in the rate on future borrowing or investment. In a hedge, you hold a futures position whose profit or loss moves opposite to the assets or liabilities you hold or plan to hold22. A borrower, who loses when rates rise, sells futures, and an investor, who loses when rates fall, buys futures.

Consider a hypothetical example in which Company A plans to borrow 100 million yen for the same three months as the reference period of a certain contract month. The interest on the loan is set by TONA compounded in arrears over that period, with no spread added. Company A now sells one contract of that contract month's interest rate futures at 99.000 (a rate of 1.000%). To keep it simple, the interest is calculated with a period of 0.25 years.

Rate for the period (% a year) Interest on the loan (yen) Futures profit or loss (yen) Combined cost (yen)
0.500 125,000 −125,000 250,000
1.000 250,000 0 250,000
1.500 375,000 125,000 250,000

If the rate rises to 1.500%, the interest on the loan grows to 375,000 yen, but the futures produce a gain of 125,000 yen, so the combined cost is 250,000 yen (1.000% a year). If instead the rate falls to 0.500%, the interest is only 125,000 yen, but the futures lose the same amount, so the combined cost is again 250,000 yen. Company A avoids the extra cost when rates rise, but gives up the benefit when rates fall23. How companies use derivatives is covered in How Corporates Use Derivatives.

Tokyo Financial Exchange envisages Three-month TONA Futures being used to hedge or substitute for over-the-counter yen interest rate swaps that reference TONA2. Futures prices also serve as an indicator of the level at which each future three-month rate is trading today2. Consider a hypothetical example in which the June contract is 99.500 and the September contract is 99.400. The three-month rate from June is trading at 0.500% and the three-month rate from September at 0.600%. A rate for a future period that is fixed today is called a forward rate24.

Gaps futures do not remove, and cash needed

A futures hedge leaves the risk that the hedged item and the futures do not move together. The risk that the difference (basis) between the cash rate and the futures price widens or narrows more than expected is called basis risk23. In the example above, the period and the reference rate of the loan were matched to the reference period of the futures, so no difference arose. In actual borrowing, the period may not line up with the futures contract month, or a spread may be added. Also, futures are fixed at 2,500 yen per 1bp per contract, which does not match the actual number of days used to calculate interest, so they do not necessarily offset exactly the same amount of interest.

The other issue is the flow of cash. Futures trading requires depositing margin to guarantee performance of obligations, and depending on market moves, additional margin may have to be deposited18. In the example above, while rates are falling, Company A may have to deposit more margin to cover mark-to-market losses before the interest on its loan has gone down.

Differences from FRAs

Interest rate futures and FRAs (forward rate agreements) both fix today the rate for a future period. What separates forwards from futures is not that both are agreements about the future, but whether they are traded on an exchange or bilaterally; the features of futures, such as standardized specifications, mark-to-market, and margin, follow from that25. The table below lists the differences specific to interest rate trades.

Item Interest rate futures FRA
Where traded On an exchange (exchange-traded derivative) Bilaterally between the parties (OTC derivative)
How terms are expressed Traded at a price of 100 minus the rate A fixed rate (the contract rate) is agreed
Size and period The size of one contract and the quarterly reference periods are fixed The parties agree on the notional amount and the period
Payment of profit or loss Profit or loss is calculated through daily mark-to-market, and after the reference period ends, the contract is cash settled on the difference between the final settlement price and the traded price A single payment is made when the rate is set at the start of the period, equal to the interest difference for the end of the period discounted to that date

The futures column follows the specifications of Osaka Exchange and Tokyo Financial Exchange32, and the FRA column follows a New York University lecture note26.

Notes

  1. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), page 21, "金利先物取引の仕組み" (How interest rate futures work), "（1） 取引の対象" ((1) Underlying). ↩

  2. Tokyo Financial Exchange, "TONA3ヵ月金利先物" (Three-month TONA Futures, in Japanese), "TONAとは" (What is TONA?), "TONA3ヵ月金利先物の商品概要" (Product outline of Three-month TONA Futures: trading unit, price quotation, reference period, final settlement, final settlement price), "TONA複利における日次累積複利および最終決済価格の計算方法" (How to calculate the daily cumulative compounding of TONA and the final settlement price), "TONA3ヵ月金利先物の活用方法" (How to use Three-month TONA Futures), and "OTC(店頭）円金利スワップ取引のヘッジツールとして" (As a hedging tool for OTC yen interest rate swaps). ↩ ↩2 ↩3 ↩4 ↩5 ↩6 ↩7 ↩8 ↩9

  3. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), page 21, "金利先物取引の仕組み" (How interest rate futures work), "（1） 取引の対象" ((1) Underlying) and "（2） 限月取引及びその数" ((2) Contract months and their number). ↩ ↩2 ↩3

  4. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), page 23, "（5） 取引単位、呼値及び制限値幅" ((5) Trading unit, quotes, and price limits), "①取引単位、呼値の単位" (① Trading unit and tick size) and "IMM指数方式" (IMM index method). ↩ ↩2

  5. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, page 263, "Part ４　金融先物・オプション取引の用語" (Part 4: Terms in financial futures and options trading), "CME（Chicago Mercantile Exchange）" ("It opened the IMM (International Monetary Market) in 1972 and launched the world's first currency futures trading," our translation). ↩

  6. Japan Exchange Group, "商品一覧（先物・オプション）" (Product list, futures and options, in Japanese), the "金利" (Interest rates) row ("100 - TONA3か月金利（Act/365、%）" (100 − three-month TONA rate (Act/365, %)) and "TONA3か月金利先物" (3-Month TONA Futures)). ↩ ↩2

  7. Tokyo Financial Exchange, "事業内容について" (Our business, in Japanese), "上場商品概要" (Overview of listed products). ↩

  8. Chicago Mercantile Exchange Inc., filing on LIBOR fallback provisions (February 9, 2021), "SOFR as Successor to USD LIBOR" (pages 4–5 of the PDF). ↩ ↩2

  9. Federal Reserve Bank of New York, "Additional Information about Reference Rates Administered by the New York Fed," "Information about the Treasury Repo Reference Rates." It describes SOFR and the New York Fed's role as administrator. ↩

  10. Alternative Reference Rates Committee, "ARRC Welcomes CME Group’s SOFR First for Options Announcement" (May 5, 2022), page 1 ("the impressive growth already seen in SOFR futures"). ↩

  11. Chicago Mercantile Exchange Inc., filing (February 9, 2021), footnote 32 (page 14 of the PDF). It describes the reference period of SOFR futures as "spanning from one Mar/Jun/Sep/Dec Quarterly IMM Wednesday to the next." ↩

  12. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, the table in "金融取の金利先物等取引の概要" (Overview of interest rate futures and related contracts on Tokyo Financial Exchange), page 15, and item ② of "差金決済" (Cash settlement), page 28. ↩

  13. Bank of Japan and Financial Services Agency, "Review of JPY LIBOR Transition and Future Initiatives" (Bank of Japan Review 2022-E-4, May 2022), page 3 ("the Tokyo Interbank Offered Rate (TIBOR)"). Source for the full English name of TIBOR. ↩

  14. Tokyo Financial Exchange, "ユーロ円3ヵ月金利先物の取引停止について" (Suspension of trading in three-month Euroyen futures, in Japanese), June 14, 2024. ↩

  15. 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" (The current state and outlook of JBA TIBOR in light of benchmark reform, in Japanese), detailed explanatory material (June 2026), the note on page 1 ("同指標は2024年12月末をもって恒久的な公表停止に至っています", publication of the rate was permanently ceased at the end of December 2024, our translation). ↩

  16. Bank of Japan and Financial Services Agency, "Review of JPY LIBOR Transition and Future Initiatives" (Bank of Japan Review 2022-E-4, May 2022), page 1 ("The London Interbank Offered Rate (LIBOR)"). Source for the full English name of LIBOR. ↩

  17. Chicago Mercantile Exchange Inc., filing (February 9, 2021), "Operation of USD LIBOR Fallbacks for CME Three-Month Eurodollar Futures" (page 12 of the PDF) and proposed Rule 45236.B. (page 26 of the PDF). ↩

  18. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, pages 7–8, "⑵ 取引所金融先物取引" ((2) Exchange-traded financial futures), items イ to ト (a to g). ↩ ↩2 ↩3

  19. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, pages 24–26, "③ 受託取引の証拠金" (③ Margin for customer trades), items イ (note ※２ on "先物の計算上の損益", calculated profit or loss on futures), ハ, and ホ. Japan Exchange Group, "顧客が差し入れる証拠金" (Margin deposited by customers, in Japanese; updated November 2, 2023), "受入証拠金の計算方法" (Calculation of margin received), "計算上の損益額" (Calculated profit or loss), "計算上の利益の払出し" (Payout of calculated profit), and "証拠金の差入れ及び維持" (Deposit and maintenance of margin). ↩

  20. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, page 30, "ｂ．金利先物等取引の最終決済の場合" (b. Final settlement of interest rate futures and related contracts), and pages 28–29, "⑽ 顧客の決済に伴う金銭の授受" ((10) Payments on customer settlement), note ※１ to item ａ (the adjustment when calculated profit has been withdrawn, which also applies to final settlement). ↩

  21. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, pages 27–28, "⑼ 取引所・取引参加者間の金利先物等取引の最終決済" ((9) Final settlement of interest rate futures and related contracts between the exchange and trading participants), "ｂ．差金決済" (b. Cash settlement) item ① and its note ("清算参加者と金融取の間および非清算参加者と清算参加者の間では", between clearing participants and Tokyo Financial Exchange and between non-clearing participants and clearing participants). ↩

  22. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, page 62, "8. 金融先物取引の利用法" (8. Uses of financial futures), "⑴ へッジ取引" ((1) Hedging). ↩

  23. Financial Futures Association of Japan, "金融先物取引の知識" (Knowledge of financial futures trading, in Japanese), 2015, pages 62–64, "〔事例１-１〕借入れ金利についてのへッジ" (Case 1-1: Hedging a borrowing rate). ↩ ↩2

  24. Bank of Japan Financial System and Bank Examination Department, Center for Advanced Financial Technology, "スポットレートとその応用" (Spot rates and their applications, in Japanese), August 2012, "４．インプライド・フォワード・レート" (4. Implied forward rates), page 12 ("現時点のスポットレートの体系から、将来の金利の予測値を導くことが可能。", the expected value of future rates can be derived from the current structure of spot rates, our translation). ↩

  25. Japan Exchange Group, "国債先物入門" (Introduction to JGB Futures, in Japanese), by Takahiro Hattori, 2021, section "2. 3 先渡（フォワード）との違い：先物の本質は取引所取引" (How futures differ from forwards: the essence of futures is exchange trading), pages 4–5. ↩

  26. Jennifer Carpenter, "Forward Rate Agreements" (lecture note, New York University Stern School of Business), page 2. It explains the fixed rate f and notional amount N, and settlement at the start of the period on a discounted amount. ↩