*The Business Professor*, updated September 20, 2019, last accessed May 31, 2020, https://thebusinessprofessor.com/lesson/call-swaption-definition/.

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### Call Swaption Definition

A swap agreement refers to a contract that allows two individuals or parties exchange or swap financial instruments. This exchange is with the aim of attending to the different needs of both parties.

In a call option, a call swaption gives its holder, usually a buyer the right to make a swap agreement with another party as the floating payer and the receiver of the fixed rate in the contract. A call swaption is also called a receiver swaption. Holders of a call swaption are not under any obligation to enter such agreements, rather, it is a right which they might choose to exercise or otherwise.

### A Little More on What is a Call Swaption

There are two types of swaptions, they are call swaption and put swaption. A call swaption is also a receiver swaption while a put swaption is a payer swaption. Swaptions are not standardized agreements or contracts, all swaptions are done over-the-counter (OTC).

Just like options, there are certain terms that parties must agree to in a swaption. Swaptions also have their strike price, expiration date and other terms contained in the agreement such as the notional amount, fixed and floating rates. Also, expiration style for swaptions differ from place to place. We have the American, Bermudan and European styles which have different features.

### Call Swaption Considerations

In a call swaption, the holder of the right needs to agree to be the floating rate payer and fixed rate receiver in the swap agreement. That means that the holder of this type of swaption exchanges its fixed-rate liability for a floating-rate liability. Hence, he pays a floating rate to the other party and receives a fixed rate from the same party. Buyers of call swaptions enter into an agreement with the aim of hedging against a potential decline in interest rates.

**Put Swaptions**

A put swaption is the opposite of a call swaption. In this swap agreement, the holder of a put swaption pays the fixed rate and receives a floating rate. Individuals or institutions that go for this swaption do so with the perception that the interest rate of the option will likely increase. Hence, they agree to pay the fixed rate to the call swaption holder in exchange for the likely profit they will realize when the floating interest rates increase.

### Reference for “Call swaption”

https://www.investopedia.com › Investing › Options

https://www.investopedia.com › Investing › Mutual Funds

https://www.nasdaq.com/investing/glossary/c/call-swaption

https://financial-dictionary.thefreedictionary.com/Call+swaption

https://quantnet.com › Forums › Quant discussion › Pricing, Modeling

### Academic research on “Call swaption”

An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and **swaption **prices**Jagannathan, R., Kaplin, A., & Sun, S. (2003). An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices. ***Journal of Econometrics***, ***116***(1-2), 113-146. ****We evaluate the classical Cox et al. (Econometrica 53(2) (1985) 385) (CIR) model using data on London Interbank Offer Rate (LIBOR), swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid–ask spread in these markets. The model overvalues shorter maturity caps and undervalues longer maturity caps. The model tends to undervalue swaptions. The magnitude of the mispricing is positively related to the magnitude of the slope of the yield curve. Our findings point out the need for evaluating term structure models using data on derivative prices.**

A unified approach to credit default **swaption **and constant maturity credit default swap valuation**Krekel, M., & Wenzel, J. (2006). A unified approach to credit default swaption and constant maturity credit default swap valuation. **In this paper we examine the pricing of arbitrary credit derivatives with the Libor Market Model with Default Risk. We show, how to setup the Monte Carlo-Simulation efficiently and investigate the accuracy of closed-form solutions for Credit Default Swaps, Credit Default Swaptions and Constant Maturity Credit Default Swaps. In addition we derive a new closed-form solution for Credit Default Swaptions which allows for time-dependent volatility and abitrary correlation structure of default intensities.

Arbitrage‐free construction of the **swaption **cube**Johnson, S., & Nonas, B. (2009). Arbitrage****‐****free construction of the swaption cube. ***Wilmott Journal: The International Journal of Innovative Quantitative Finance Research***, ***1***(3), 137-143. ****In this paper we look at two areas in the interest rate options market where arbitrage could be hiding. In the first section we derive a no****‐****arbitrage condition for swaption prices with complementary expiry dates and tenors within the swaption cube. In the second section we propose an alternative European option approximation for the widely used SABR dynamics that reduces the possibility of arbitrage for long maturities and low strikes. Copyright © 2009 Wilmott Magazine Ltd**

Which process gives rise to the observed dependence of **swaption **implied volatility on the underlying?** Rebonato, R. (2003). Which process gives rise to the observed dependence of swaption implied volatility on the underlying?. ***International Journal of Theoretical and Applied Finance***, ***6***(04), 419-442. **In this paper we investigate whether a CEV model can account for the observed variation in the at-the-money implied volatility as a function of the level of the at-the-money forward rate. We also determine which exponent β in the CEV process for the swap rate best accounts for the observed behaviour of the implied volatilities.

The effects of quantitative easing on interest rates: channels and implications for policy**Krishnamurthy, A., & Vissing-Jorgensen, A. (2011). ***The effects of quantitative easing on interest rates: channels and implications for policy*** (No. w17555). National Bureau of Economic Research. ****The outstanding face amount of plain vanilla interest rate swaps exceeds two trillion dollars. While pricing and hedging of such swaps appear to be quite simple, many existing theories are based on the incorrect characterization of a swap as a simple exchange of a fixed for a floating rate note. This characterization is not consistent with standarized swap contracts and the treatment of swaps in bankruptcy. This paper provides an alternative perspective on swaps.**