Interest rate swap: Difference between revisions

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==Types==

==Types==

Common structures include the following.<ref>{{cite web |title=Interest Rate Swaps: Cleared and Customized |url=https://www.isda.org/a/Ly9TE/IRS-Cleared-and-Customized.pdf |website=International Swaps and Derivatives Association |date=1 July 2020 |access-date=14 October 2025}}</ref><ref>{{cite web |title=2021 ISDA Interest Rate Derivatives Definitions |url=https://www.isda.org/2021/10/04/2021-isda-interest-rate-derivatives-definitions/ |website=International Swaps and Derivatives Association |date=4 October 2021 |access-date=14 October 2025}}</ref>

* Fixed-for-floating swaps exchange a fixed rate for a floating index in the same currency.

* Fixed-for-floating swaps exchange a fixed rate for a floating index in the same currency.

* Basis swaps exchange a floating rate for a floating rate of a different tenor of the same index.

* Basis swaps exchange a floating rate for a floating rate of a different tenor of the same index.

* Overnight index swaps pay a fixed rate versus a compounded overnight risk-free rate such as SOFR, SONIA or €STR.

* Overnight index swaps pay a fixed rate versus a compounded overnight risk-free rate such as SOFR, SONIA or €STR.

* Forward-start and deferred-start swaps begin on a future date.

* Forward-start and deferred-start swaps begin on a future date.

* Amortising and accreting swaps use notionals that change over time.

* Amortising and accreting swaps use notionals that change over time.

* Constant-maturity swaps link one leg to a constant-maturity swap rate.

* Constant-maturity swaps link one leg to a constant-maturity swap rate.

==Uses==

==Uses==

Linear interest rate derivative involving exchange of interest rates between two parties

An interest rate swap is a derivative contract in which two parties exchange streams of interest payments on a notional principal for a set period. The most common form exchanges a fixed rate for a floating rate in the same currency. Variants include basis swaps, overnight index swaps (OIS), forward-start swaps and swaps with changing notionals. Since the late 2000s, collateralised swaps are typically priced and risk-managed using OIS discounting, and following the end of LIBOR new trades reference overnight risk-free rates such as the SOFR, the SONIA and the €STR. As at end-June 2024, interest rate derivatives were the largest segment of the global over-the-counter derivatives market by notional outstanding.^[1][2][3]

History

Arrangements resembling swaps emerged from back-to-back or parallel loans used in the 1970s to navigate exchange controls. A widely cited early landmark was a 1981 currency swap between IBM and the World Bank arranged by Salomon Brothers, which helped popularise the technique.^[4][5] The first interest rate swap is commonly dated to 1982.^[6]

Standard documentation and definitions from ISDA in the 1990s and 2000s supported market growth and common terminology.^[7] After the 2007–2008 crisis, pricing for collateralised swaps shifted to OIS discounting and multi-curve approaches, reflecting the role of collateral and funding costs.^[8]

From 2021 to 2024, regulators completed the transition from LIBOR to overnight risk-free rates. Remaining synthetic sterling and United States dollar LIBOR settings ceased in 2024, which marked the end of LIBOR in mainstream use.^[9][10]

Mechanics

A standard interest rate swap has two legs linked to the same notional amount. The fixed leg pays a fixed rate on scheduled accrual periods. The floating leg pays a rate set at each reset date by a reference index such as SOFR, SONIA or €STR, with payments exchanged on the corresponding payment dates. Day-count and business-day conventions follow market standards defined in documentation such as the ISDA Interest Rate Derivatives Definitions and, for on-venue trading, the relevant rulebooks.^[11][12]

Variants include forward-start swaps, amortising or accreting notionals, zero-coupon swaps, basis swaps in which both legs float, and overnight index swaps that reference a compounded overnight rate.

Types

Common structures include the following.^[13][14]

• Fixed-for-floating swaps exchange a fixed rate for a floating index in the same currency.
• Basis swaps exchange a floating rate for a floating rate of a different tenor of the same index.
• Overnight index swaps pay a fixed rate versus a compounded overnight risk-free rate such as SOFR, SONIA or €STR.
• Forward-start and deferred-start swaps begin on a future date.
• Amortising and accreting swaps use notionals that change over time.
• Constant-maturity swaps link one leg to a constant-maturity swap rate.

Uses

Common uses include hedging interest rate exposure, adjusting asset and liability duration, and expressing views on the level or shape of the yield curve. In United States markets, the futures and swaps ecosystem now links SOFR futures and SOFR-linked swaps after the conversion of Eurodollar contracts and USD LIBOR swaps in 2023.^[15]

Valuation and pricing

A vanilla fixed-for-floating swap has a value equal to the difference between the present value of the fixed leg and the present value of the floating leg, discounted on the appropriate curve.

The present value of the fixed leg is

${\displaystyle P_{\text{fixed}}=N\sum _{i=1}^{n}K\,\alpha _{i}\,D(0,t_{i})}$

where ${\displaystyle N}$ is notional, ${\displaystyle K}$ is the fixed rate, ${\displaystyle \alpha _{i}}$ are accrual fractions, ${\displaystyle t_{i}}$ are payment dates and ${\displaystyle D(0,t)}$ are discount factors.

Under a standard par-swap set-up, the floating leg can be written using forward rates ${\displaystyle F_{j}}$ and discount factors:

${\displaystyle P_{\text{float}}=N\sum _{j=1}^{m}F_{j}\,\beta _{j}\,D(0,u_{j})}$

The par swap rate ${\displaystyle S}$ that sets the swap’s value to zero is

${\displaystyle S={\dfrac {\sum _{j=1}^{m}F_{j}\,\beta _{j}\,D(0,u_{j})}{\sum _{i=1}^{n}\alpha _{i}\,D(0,t_{i})}}}$

For a quoted swap with fixed rate ${\displaystyle R}$, the mark-to-market is often written

${\displaystyle P_{\text{IRS}}=N\,(R-S)\,A}$

with ${\displaystyle A=\sum _{i=1}^{n}\alpha _{i}\,D(0,t_{i})}$.

Following the financial crisis, collateralised swaps are commonly discounted using the overnight index swap curve that matches the collateral rate specified under the credit support annex. This leads to multi-curve frameworks that separate discounting from forward-rate projection.^[16][17]

Market structure and regulation

A large share of plain-vanilla swaps is centrally cleared, with clearing mandates and reporting rules in major jurisdictions. In the United States, the Commodity Futures Trading Commission updated the clearing requirement in 2022 to reflect the transition to risk-free rates and added SOFR overnight index swaps across standard maturities.^[18] In the European Union, reforms under EMIR 3.0 introduce an active account requirement intended to ensure EU market participants maintain and use accounts at EU central counterparties for specified interest rate derivatives.^[19]

Market convention summaries for on-venue trading are published by swap execution facilities and multilateral trading facilities.^[20]

Conventions by currency

Typical fixed-leg conventions for vanilla swaps vary by currency. Actual terms depend on documentation and venue rules.

Currency	Typical fixed-leg frequency	Typical fixed-leg day count	Common floating index
USD	Semi-annual	30/360	SOFR (compounded)
EUR	Annual	30/360	€STR (compounded) or EURIBOR (legacy)
GBP	Semi-annual	ACT/365F	SONIA (compounded)
JPY	Annual	ACT/365F	TONA (compounded)

Risks

Interest rate swaps expose traders and institutions to various categories of financial risk:^[21] predominantly market risk – specifically interest rate risk – and credit risk. Reputation risks also exist. The mis-selling of swaps, over-exposure of municipalities to derivative contracts, and IBOR manipulation are examples of high-profile cases where trading interest rate swaps has led to a loss of reputation and fines by regulators.

As regards market risk, during the swap’s life, both the discounting factors and the forward rates change, and thus, per the above valuation techniques, the PV of a swap will deviate from its initial value. The swap will therefore at times be an asset to one party and a liability to the other. (The way these changes in value are reported is the subject of IAS 39 for jurisdictions following IFRS, and FAS 133 for U.S. GAAP.) In market terminology, the first-order link of swap value to interest rates is referred to as delta risk; their gamma risk reflects how delta risk changes as market interest rates fluctuate (see Greeks (finance)). Other specific types of market risk that interest rate swaps have exposure to are basis risks, where various IBOR tenor indexes can deviate from one another, and reset risks, where the publication of specific tenor IBOR indexes are subject to daily fluctuation.

Uncollateralised interest rate swaps — those executed bilaterally without a CSA in place — expose the trading counterparties to funding risks and counterparty credit risks.^[22] Funding risks because the value of the swap might deviate to become so negative that it is unaffordable and cannot be funded. Credit risks because the respective counterparty, for whom the value of the swap is positive, will be concerned about the opposing counterparty defaulting on its obligations. Collateralised interest rate swaps, on the other hand, expose the users to collateral risks: here, depending upon the terms of the CSA, the type of posted collateral that is permitted might become more or less expensive due to other extraneous market movements. Credit and funding risks still exist for collateralised trades but to a much lesser extent. Regardless, due to regulations set out in the Basel III Regulatory Frameworks, trading interest rate derivatives commands a capital usage. The consequence of this is that, dependent upon their specific nature, interest rate swaps may be capital intensive; with the latter, also, sensitive to market movements. Capital risks are thus another concern for users, and Banks typically calculate a credit valuation adjustment, CVA – as well as XVA for other risks – which then incorporate these risks into the instrument value.^[23]

Debt security traders, daily mark to market their swap positions so as to “visualize their inventory” (see valuation control).
As required, they will attempt to hedge, both to protect value and to reduce volatility. Since the cash flows of component swaps offset each other, traders will implement this hedging on a net basis for entire books.^[24] Here, the trader would typically hedge her interest rate risk through offsetting Treasuries (either spot or futures).
For credit risks – which will not typically offset – traders estimate:^[22]
for each counterparty the probability of default using models such as Jarrow–Turnbull and KMV, or by stripping these from CDS prices;
and then for each trade, the potential future exposure and expected exposure to the counterparty.
Credit derivatives will then be purchased ^[22] as appropriate.
Often, a specialized XVA-desk centrally monitors and manages overall CVA and XVA exposure and capital, and will then implement this hedge.^[25]
The other risks must be managed systematically, sometimes involving group treasury.

These processes will all rely on well-designed numerical risk models: both to measure and forecast the (overall) change in value, and to suggest reliable offsetting benchmark trades which may be used to mitigate risks. Note, however, (and re P&L Attribution) that the multi-curve framework adds complexity ^[26] in that (individual) positions are (potentially) affected by numerous instruments not obviously related.

Quotation and market-making

ICE Swap rate

ICE Swap rate^[27] replaced the rate formerly known as ISDAFIX in 2015. Swap Rate benchmark rates are calculated using eligible prices and volumes for specified interest rate derivative products. The prices are provided by trading venues in accordance with a “Waterfall” Methodology. The first level of the Waterfall (“Level 1”) uses eligible, executable prices and volumes provided by regulated, electronic, trading venues. Multiple, randomised snapshots of market data are taken during a short window before calculation. This enhances the benchmark’s robustness and reliability by protecting against attempted manipulation and temporary aberrations in the underlying market.^{[citation needed]}

Market-making

The market-making of IRSs is an involved process involving multiple tasks; curve construction with reference to interbank markets, individual derivative contract pricing, risk management of credit, cash and capital. The cross disciplines required include quantitative analysis and mathematical expertise, disciplined and organized approach towards profits and losses, and coherent psychological and subjective assessment of financial market information and price-taker analysis. The time sensitive nature of markets also creates a pressurized environment. Many tools and techniques have been designed to improve efficiency of market-making in a drive to efficiency and consistency.^[21]

See also

References

Further reading

General:

Early literature on the incoherence of the one curve pricing approach:

Multi-curves framework:

• Henrard M. (2007). The Irony in the Derivatives Discounting, Wilmott Magazine, pp. 92–98, July 2007. SSRN preprint.
• Kijima M., Tanaka K., and Wong T. (2009). A Multi-Quality Model of Interest Rates, Quantitative Finance, pages 133-145, 2009.
• Henrard M. (2010). The Irony in the Derivatives Discounting Part II: The Crisis, Wilmott Journal, Vol. 2, pp. 301–316, 2010. SSRN preprint.
• Bianchetti M. (2010). Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves, Risk Magazine, August 2010. SSRN preprint.
• Henrard M. (2014) Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution, and Implementation. Palgrave Macmillan. Applied Quantitative Finance series. June 2014. ISBN 978-1-137-37465-3.

External links

and are regarded as an