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CMS swaps in separable one-factor Gaussian LLM and HJM model

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  • Henrard, Marc

Abstract

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LLM and HJM models is presented. The approximation used is a Taylor expansion on the swap rate as a function of a random variable which is intuitively similar to a (short) rate. This approach is different from the standard approach in CMS where the discounting is written as a function of the swap rate. The approximation is very efficient.

Suggested Citation

  • Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3228
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    File URL: https://mpra.ub.uni-muenchen.de/3228/1/MPRA_paper_3228.pdf
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    References listed on IDEAS

    as
    1. Henrard, Marc, 2007. "Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options," MPRA Paper 1534, University Library of Munich, Germany.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    3. Marc Henrard, 2006. "A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 1-18.
    4. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    5. Marc Henrard, 2003. "Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 57-72.
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    Cited by:

    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. 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.
    3. Bin Chen & Cornelis W. Oosterlee & Sacha Van Weeren, 2010. "Analytical Approximation To Constant Maturity Swap Convexity Corrections In A Multi-Factor Sabr Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 1019-1046.

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    More about this item

    Keywords

    CMS swap; LLM model; HJM model; one factor; approximation;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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