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Mathematical foundation of convexity correction

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Abstract

A broad class of exotic interest rate derivatives can be valued simply by adjusting the forward interest rate. This adjustment is known in the market as convexity correction. Various ad hoc rules are used to calculate the convexity correction for different products, many of them mutually inconsistent. In this research paper we put convexity correction on a firm mathematical basis by showing that it can be interpreted as the side-effect of a change of probability measure. This provides us with a theoretically consistent framework to calculate convexity corrections. Using this framework we review various expressions for LIBOR in arrears and diff swaps that have been derived in the literature. Furthermore, we propose a simple method to calculate analytical approximations for general instances of convexity correction.

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  • A. Pelsser, 2003. "Mathematical foundation of convexity correction," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 59-65.
    • Handle: RePEc:taf:quantf:v:3:y:2003:i:1:p:59-65
    DOI: 10.1088/1469-7688/3/1/306
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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    3. Rudiger Frey & Daniel Sommer, 1996. "A systematic approach to pricing and hedging international derivatives with interest rate risk: analysis of international derivatives under stochastic interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 295-317.
    4. Marek Rutkowski, 1998. "Dynamics of Spot, Forward, and Futures Libor Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 425-445.
    5. Eric Benhamou, 2002. "A Martingale Result for Convexity Adjustment in the Black Pricing Model," Finance 0212005, University Library of Munich, Germany.
    6. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    1. Jiří Witzany, 2009. "Valuation of Convexity Related Interest Rate Derivatives," Prague Economic Papers, Prague University of Economics and Business, vol. 2009(4), pages 309-326.
    2. Keiichi Tanaka & Takeshi Yamada & Toshiaki Watanabe, 2010. "Applications of Gram-Charlier expansion and bond moments for pricing of interest rates and credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 645-662.
    3. López, Oscar & Oleaga, Gerardo & Sánchez, Alejandra, 2021. "Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    4. Oscar Lopez & Gerardo E. Oleaga & Alejandra Sanchez, 2019. "Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bonds," Papers 1901.02995, arXiv.org.
    5. Antoine Jacquier & Mugad Oumgari, 2023. "Interest rate convexity in a Gaussian framework," Papers 2307.14218, arXiv.org, revised Mar 2024.
    6. Schrager, David F. & Pelsser, Antoon A.J., 2004. "Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 369-398, October.
    7. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    8. Leccadito, Arturo & Tunaru, Radu S. & Urga, Giovanni, 2015. "Trading strategies with implied forward credit default swap spreads," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 361-375.
    9. Nikolaos Karouzakis & John Hatgioannides & Kostas Andriosopoulos, 2018. "Convexity adjustment for constant maturity swaps in a multi-curve framework," Annals of Operations Research, Springer, vol. 266(1), pages 159-181, July.
    10. Yang, Sharon S. & Yueh, Meng-Lan & Tang, Chun-Hua, 2008. "Valuation of the interest rate guarantee embedded in defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 920-934, June.

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