Forward Rate Agreements (FRA)

An FRA is a trade that lets a company planning to borrow fix its borrowing rate in advance. It can also be seen as an interest rate swap broken into separate periods.

An agreement that fixes the rate for a future period today

An FRA (forward rate agreement) is a transaction that fixes the interest rate for a set future period today. In Japanese it is called kinri sakiwatashi torihiki¹. Like an interest rate swap, it is an OTC derivative on interest rates². It shares with a forward contract the feature of fixing future terms today³. Forwards in general are covered in Forwards and Futures. The fixed rate agreed today is called the contract rate.

Consider a hypothetical example in which Company D and Bank E enter into an FRA with a notional amount of 10 billion yen that fixes at 1% a year the rate for a 6-month period starting 6 months from now. Company D is the buyer and Bank E is the seller. If the 6-month benchmark rate fixed 6 months from now is higher than 1% a year, Bank E pays Company D. If it is lower, Company D pays Bank E. Either way, one payment is made, based on the difference between the two rates⁴. Neither party pays the notional amount of 10 billion yen itself.

The amount exchanged is the product of the notional amount, the difference between the benchmark rate and the contract rate, and the length of the period⁵. The next section shows the calculation. A master agreement form drawn up by a European banking association also sets the direction of payment as in the example⁶. In other words, the buyer is in the same position as a party that pays the contract rate and receives the benchmark rate.

The period of an FRA is written as two numbers of months, such as "3×6": the months from today to the start of the period and the months from today to its end. A 3×6 FRA fixes the rate today for a 3-month period starting 3 months from now⁷. In this notation, the FRA in the example is a 6×12 FRA.

Paying the discounted difference on the settlement date

The amount of the difference is known once the benchmark rate is fixed at the start of the period, so the parties settle it at the start rather than waiting until the end. The amount paid is the interest difference for the end of the period, discounted at the benchmark rate that has just been fixed⁸. This date at the start of the period is called the settlement date.

In the 10 billion yen example, suppose the benchmark rate fixed 6 months from now is 2% a year. With a period length of 0.5 years, the interest difference at the end of the period is 10 billion yen × (2% − 1%) × 0.5 = 50 million yen. Divided by 1 + 2% × 0.5 = 1.01, this gives about 49.50 million yen, which Bank E pays Company D on the settlement date⁹. If the benchmark rate is 0.5% a year, the interest difference is −25 million yen, and Company D pays Bank E about 24.94 million yen.

In general, the settlement amount is given by the following formula.

$$\text{Settlement amount} = \frac{\text{Notional amount} \times (\text{Benchmark rate} - \text{Contract rate}) \times \text{Period length (years)}}{1 + \text{Benchmark rate} \times \text{Period length (years)}}$$

The numerator is the interest difference that would be exchanged at the end of the period. Dividing by the denominator converts it to its value at the start of the period. If the settlement amount is positive, the seller pays the buyer. If it is negative, the buyer pays the seller its absolute value.

To keep the arithmetic simple, the example uses a period length of 0.5 years. In actual trades, the number of days in the period is converted into years using the day count convention the parties choose¹⁰.

The contract rate of an FRA and the forward rate

When an FRA is agreed, the contract rate is set at the rate that makes the value of the FRA zero. That rate equals the forward rate, the rate for a future period calculated from today's rates for different periods¹¹.

Settling the discounted amount at the start of the period gives the FRA the same value as settling at the end⁸. If the amount received at the start is invested until the end of the period at the benchmark rate that has been fixed, it grows to the interest difference at the end. In the 10 billion yen example, investing 49.50 million yen for 0.5 years at 2% a year gives 49.50 million yen × 1.01, or about 50 million yen.

An interest rate swap can be viewed as a series of FRAs covering successive periods¹². For a 2-year interest rate swap with semiannual payments, paying the fixed rate and receiving the floating rate can be split into four FRAs: 0×6, 6×12, 12×18, and 18×24. In a series of FRAs, however, each period's contract rate is the forward rate for that period¹¹, while an interest rate swap uses the same fixed rate for every period¹³.

Value after rates move

After an FRA is agreed, if market rates move and the forward rate for the period rises, the buyer's value rises and the seller's value falls by the same amount. If the forward rate falls, the reverse happens. When the FRA is agreed, the contract rate equals the forward rate and the value is zero. After that, the value depends on the difference between the contract rate and the current forward rate¹¹.

The simulator below builds a yield curve, the set of interest rates for different periods, from market rates (the overnight rate and the fixed rates of OIS for different periods), and calculates the forward rate and value of an FRA. An OIS is an interest rate swap that exchanges a fixed rate for a floating rate calculated by compounding the overnight rate¹⁴.

The default is the buyer of a 6×12 FRA with a notional amount of 10 billion yen and a contract rate of 1% a year. At the default market rates, the forward rate for the 6-month period starting in 6 months is 0.60%. Because the contract rate is above this, the buyer's value is −19,911,863 yen. If you raise the 1-year OIS rate from 0.60% to 1.20%, the forward rate becomes 1.20% and the buyer's value becomes 9,799,224 yen.

Using an FRA to fix the rate on future borrowing

Buying an FRA lets a borrower fix the rate on a future loan today. If a company planning to borrow at a floating rate buys an FRA, it receives the difference from the FRA when the benchmark rate rises and pays the difference when the rate falls. The combined rate on the loan and the FRA is therefore roughly the contract rate¹³. It is exactly the contract rate if the loan has no spread over the benchmark rate and the amount exchanged on the settlement date can be invested or funded until the maturity date at the same benchmark rate.

Suppose Company D plans to borrow 10 billion yen from Bank F for 6 months, starting 6 months from now, at the 6-month benchmark rate fixed at that time (with no spread). Company D has bought from Bank E the 6×12 FRA from the example above, with a contract rate of 1% a year. Assume that the amount exchanged on the settlement date can be invested or funded until the maturity date at the same benchmark rate.

Figure description

This shows Company D's cash flows on the FRA and the loan, in time order, when the benchmark rate is 2% a year. Nothing is exchanged on the trade date. On the settlement date Company D receives the FRA difference from Bank E, and on the maturity date it pays the loan interest to Bank F. The amounts are the same as in the calculation in the text below.

If the benchmark rate rises to 2% a year, Company D pays 100 million yen of interest on the loan. The amount received from the FRA grows to about 50 million yen by the maturity date, so the net cost is about 50 million yen, the same as borrowing at 1% a year. Without the FRA, Company D would have paid 100 million yen, so it is about 50 million yen better off.

If the benchmark rate falls to 0.5% a year, the loan interest is only 25 million yen, but Company D pays about 24.94 million yen on the FRA on the settlement date. That amount is worth about 25 million yen at the maturity date, so the net cost is again about 50 million yen (1% a year). Without the FRA, Company D would have paid only 25 million yen, so it is about 25 million yen worse off. The gain or loss of the seller, Bank E, is the opposite of Company D's gain or loss on the FRA. How corporates use hedges is covered in How Corporates Use Derivatives.

Risks and the market today

Because an FRA is traded over the counter, there is a risk that the other party cannot pay the difference on the settlement date. The difference is exchanged only once, on that date, so if the other party cannot pay then, the receiver does not get it.

A Bank of Japan paper shows that FRAs made up 15.3% of global OTC derivatives outstanding at the end of June 2020¹. At the end of June 2026, major dealers in Japan held FRAs with a notional amount of about 4.1 trillion US dollars, about 5.0% of their OTC interest rate derivatives of about 81.9 trillion US dollars. The breakdown is as follows¹⁵.

By counterparty, 96.9% of all FRAs (about 3.9 trillion US dollars) were with central counterparties.

A university lecture note that shows amounts outstanding for 2009 said that most FRAs were linked to LIBOR (London Interbank Offered Rate) or EURIBOR¹⁶. The US Commodity Futures Trading Commission (CFTC) requires four classes of FRAs to be cleared. As of September 1, 2026, the table in its rule lists EURIBOR (euro), WIBOR (Polish zloty), NIBOR (Norwegian krone), and STIBOR (Swedish krona) as their benchmark rates¹⁷.

Notes

1. Bank of Japan, "店頭デリバティブ取引データからみた円金利スワップ市場" (The yen interest rate swap market seen through OTC derivatives trade data, in Japanese; Bank of Japan Review 2021-J-7, June 2021), Chart 1 "店頭デリバティブ取引の商品種類別構成比" (Composition of OTC derivatives by product type), page 1. The chart shows shares of amounts outstanding at the end of June 2020 (global basis), based on the BIS regular statistics. ↩ ↩²

2. Federal Reserve Bank of New York, Staff Report No. 557 (2012), the product classification "Forward rate agreements (FRA)" (page 6 of the PDF). ↩

3. Jennifer Carpenter, "Forward Rate Agreements" (lecture note, New York University Stern School of Business), pages 2–3. It says that in an FRA the fixed rate and the notional amount are set at the start of the trade and the exchange takes place on a single future date. The definition of a forward contract is in the glossary entry "Forward contract". ↩

4. Jennifer Carpenter, "Forward Rate Agreements" (lecture note, New York University Stern School of Business), page 2. It describes an FRA as a contract between two parties to exchange a fixed interest payment and a floating interest payment on a single date. ↩

5. European Banking Federation, supplement for interest rate transactions "Interest Rate Transactions" (Edition 2020), the definition of an FRA in Section 2, and Sections 4(2) and 4(5)(a) (pages 1–3). It sets the floating amount of an FRA as the product of the principal, the rate difference, and the day count fraction. ↩

6. The same document, Section 3(2) "Forward Rate Agreement" (page 2). ↩

7. Donald J. Smith, "A Teaching Note on Pricing and Valuing Interest Rate Swaps Using LIBOR and OIS Discounting" (June 2012), page 9. It gives "a 3x 6 FRA" as an example that fixes the rate for a 3-month period starting in 3 months. ↩

8. Jennifer Carpenter, "Forward Rate Agreements", page 2. It says that settling the interest difference at the end of the period at the start, divided by (1 + r/2), does not change the value. ↩ ↩²

9. 50,000,000 yen ÷ 1.01 = 49,504,950.4… yen, and 25,000,000 yen ÷ 1.0025 = 24,937,655.8… yen. The table and text round these to the nearest 10,000 yen (two decimal places in millions of yen). ↩

10. The European Banking Federation supplement (Edition 2020), Section 4(2) (page 2). It sets the floating amount as the product of the principal, the rate, and the day count fraction chosen by the parties. ↩

11. Jennifer Carpenter, "Forward Rate Agreements", page 3. It expresses the value of an FRA as a combination of discount bonds and says that the fixed rate that makes the value zero at inception is the forward rate. ↩ ↩² ↩³

12. The same document, page 4. It says that the cash flow for each period of a swap is the cash flow of an FRA whose fixed rate is the swap rate. ↩

13. Donald J. Smith, "A Teaching Note on Pricing and Valuing Interest Rate Swaps Using LIBOR and OIS Discounting" (June 2012), page 9. It says that a floating-rate liability can be made fixed with a strip of FRAs that pay the fixed rate or with an interest rate swap. With FRAs the rate varies by period, and with a swap the fixed rate is the same for every period. ↩ ↩²

14. Study Group on Risk-Free Reference Rates, "日本円ＯＩＳ（Overnight Index Swap）─取引の概要と活用事例─" (Japanese yen OIS: overview and use cases, information as of March 2018, in Japanese), "（OIS の定義）" (Definition of OIS) under "２．OIS とは何か" (What is OIS), page 3 (page 5 of the PDF). ↩

15. Bank of Japan Financial Markets Department, "「デリバティブ取引に関する定例市場報告」日本分集計結果（2026年6月末）" (Detailed Data for the Regular Derivatives Market Statistics in Japan, end-June 2026, in Japanese; September 10, 2026), Table 2 "金利関連取引" (Interest rate derivatives). The unit is millions of US dollars; this page converts them to trillions or billions and rounds the shares to one decimal place. English version: "Detailed Data", Table 2 "Interest rate derivatives". ↩

16. Jennifer Carpenter, "Forward Rate Agreements", page 2. The document is undated, and the same page shows amounts of FRAs outstanding in 2009. ↩

17. 17 CFR 50.4(a), Table 3 "Forward rate agreement class". Checked against the text in the Electronic Code of Federal Regulations as of September 1, 2026. ↩