*The Business Professor*, updated September 20, 2019, last accessed May 28, 2020, https://thebusinessprofessor.com/lesson/accrual-swap-definition/.

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**Accrual Swap Definition**

The accrual swap refers to a type of interest rate swap where interest accrues and is paid to one counterpart (one side) as long as the reference rate stays within the determined index rate range. In this kind of rate, one counterpart meets the cost of the standard floating reference rate, and he or she gets the reference rate with the addition of a spread. Interest payment for counter counterpart accrues for days only if the reference rate remains with a predetermined range. Other terms used to refer to an accrual swap include range accrual swaps or corridor accrual swap.

### A Little More on What is an **Accrual Swap**

Accrual swaps use different time intervals such as a month, two months, six months or even twelve months London Interbank Offered Rate (LIBOR) for the reference. However, the ten years period is also applicable when treasury rates are used. Note that the range must always be predetermined and in some cases, it may be permanently fixed throughout a swap’s life.

Nonetheless, this does not mean that the reference rate can’t be reset. It can be reset but depending on various swap factors such as the kind of the accrual swap as well as the accrual swap’s terms one is dealing with. The resetting is done at a fixed date though in most cases, it takes place during the coupon date.

**Types of Accrual Swap**

**Binary accrual swaps**

The binary accruals swaps refer to binary cap and binary floor. The two are financial instruments used by investors to offset any unfavorable investment risk resulting from price movement.

Besides accrual swap having an element of interest rate swap, it is also binary in nature as it includes a set of binary options. The price movement, in this case, can be upward or downward. The binary cap and floor, therefore, help investors to guard against unfavorable up and down price movement that is likely to affect their investment.

For instance, if the interest rate happens goes higher beyond the floor, payment will be initiated. On the other hand, if the rate of interest passes the cap, then payment will not be necessary. In other words, any price movement that does not stay within the preset range annuls any accruals in the future.

This means that in accrual swap, payment may or may not be paid depending on the binary prevailing circumstance. The best way an investor may use the binary option to offset the risk of price movement is to invest in two bonds which are negatively associated.

**A callable range accrual swap**

In this type of an accrual swap, one of the parties paying the accrual coupon is given the right with no obligation to revoke the swap. The cancellation of the swap can be done on any given coupon date but usually before the deadline period. Note that it is only the party with the obligation to pay the range accrual leg that has the right to cancel the swap before maturity.

Also, this swap pays the purchaser a coupon that accrues only if a preset index is able to meet a specific condition that is decided on the trading date. This means that the payment can only be done if the preset index meets the conditions put in place.

Generally, the accrual swap awards the investor a higher coupon which makes it popular. This is so because, when the cap moves to a high level, it increases the likelihood of the index moving beyond the range. This, therefore, results in an investor getting a high coupon. Similarly, when the range narrows, the coupon becomes larger.

**Fixed rate accrual swap**

Fixed rate accrual swap refers to where the payoff of a fixed accrual coupon is dependent on the length of time the reference rate stays within a set range. In this case, the accrual coupon rate remains fixed throughout a swap’s life.

**Floating rate accrual swap**

Floating rate accrual swap represents a reference rate which is not stable. Meaning, that the reference rate does not stay in the required preset range.

Due to its floating habit, a fresh reference rate is put in place whenever the accrual time is reached. This ensures that they move alongside each other during the reference rate movement.

**Uses of Accrual Swap**

An accrual swap may be used in the following two ways:

- For investment purposes
- For liability management purposes.

**The Bottom Line**

Generally, the investors and the firms who make use of accrual swaps are usually optimistic that the reference rate will remain in a given range. According to them, the wider the binary floor and upper cap is, the better. When it is wide, it enables the reference rate to stay within the range. This way there will be no accrued interest.

### Reference for “Accrual Swap”

https://www.investopedia.com › Investing › Alternative Investments

www.iotafinance.com/en/Financial-Definition-accrual-swap.html

www.forexbite.com/trading-courses/forexdictionary-Accrual-Swap-3

https://www.investment-and-finance.net/derivatives/a/accrual-swap

https://www.financialencyclopedia.net/derivatives/r/range-accrual-swap.html

www.oxfordreference.com/view/10.1093/oi/authority.20110803095346627

### Academic research on “Accrual Swap”

Pricing of range **accrual swap **in the quantum finance Libor Market Model, **Baaquie, B. E., Du, X., Tang, P., & Cao, Y. (2014). Pricing of range accrual swap in the quantum finance Libor Market Model. ***Physica A: Statistical Mechanics and its Applications***, ***401***, 182-200.**

We study the range accrual swap in the quantum finance formulation of the Libor Market Model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. The price of accrual swap is analyzed by generating daily sample values by simulating a two dimension Gaussian quantum field.

Accrual swaps and range notes, **Hagan, P. S. (2004). ***Accrual swaps and range notes***. Bloomberg Technical Report.**

Valuing credit default **swaps **I: No counterparty default risk, **Hull, J. C., & White, A. (2000). Valuing credit default swaps I: No counterparty default risk. **This paper provides a methodology for valuing credit default swaps when the payoff is contingent on default by a single reference entity and there is no counterparty defaultrisk. The paper tests the sensitivity of credit default swap valuations to assumptions about the expected recovery rate. It also tests whether approximate no-arbitrage arguments give accurate valuations and provides an example of the application of the methodology to real data. In a companion paper entitled Valuing Credit Default Swaps II: Modeling Default Correlation, the analysis is extended to cover situations where the payoff is contingent on default by multiple reference entities and situations where there is counterparty defaultrisk.

OTC derivatives and central clearing: can all transactions be cleared?, **Hull, J. (2010). OTC derivatives and central clearing: can all transactions be cleared?. ***Financial Stability Review***, ***14***, 71-78. **The 2007-2009 fi nancial crisis has led legislators on both sides of the Atlantic to propose laws that would require most “standardised” over-the-counter (OTC) derivatives to be cleared centrally. This paper examines these proposals. Although OTC derivatives did not cause the crisis, they do facilitate large speculative transactions and have the potential to create systemic risk. The main attraction of the central clearing proposals is that they will make positions in standardised derivatives more transparent. However, our experience from the 2007-2009 crisis suggests that large losses by fi nancial institutions often arise from their positions in non-standard OTC derivatives. The paper argues that one way forward for regulators is to require all OTC derivatives (standard and non-standard) to be cleared centrally within three years. This would maximise the benefi ts of netting and reduce systemic risk while making it easier for regulators to carry out stress tests. The paper divides OTC derivatives into four categories and suggests how each category could be handled for clearing purposes.

Pricing of interest rate derivatives and calibration issues in a multi-factor LIBOR market model framework, **Doubrava, J. (2007). Pricing of interest rate derivatives and calibration issues in a multi-factor LIBOR market model framework. **Financial derivatives are financial instruments which enable investor or a debtor to optimize his/her asset/debt portfolios according to individual needs and acceptable scale of risk. Their importance in financial markets rose enormously n past ten years as well as did their traded volumes. Interest rate derivatives form a large sub-group of financial derivatives, their valuation is a large self-contained chapter within financial mathematics thanks to the unique characteristics of yield- and discount-curve dynamics. In the first part of my thesis I derive the fundamental pricing principles stemming from no- arbitrage pricing theory and introduce the most common approaches in yield curve modeling. In the second part I discuss issues of calibration in a "LIBOR Market Model" with one to three risk factors. These models are used to price swaptions with Monte Carlo simulation within the no-arbitrage framework introduced in the first part. The result of the thesis is that one factor model performs the best in pricing swaptions. Powered by TCPDF (www.tcpdf.org)