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Pricing convexity adjustment with Wiener chaos

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  • Benhamou, Eric

Abstract

This paper presents an approximated formula of the convexity adjustment of Constant Maturity Swap rates, using Wiener Chaos expansion, for multi-factor lognormal zero coupon models. We derive closed formulae for CMS bond and swap and apply results to various well-known one-factor models (Ho and Lee (1986), Amin and Jarrow(1992), Hull and White (1990), Mercurio and Moraleda (1996)). Quasi Monte Carlo simulations confirm the efficiency of the approximation. Its precision relies on the importance of second and higher order terms.

Suggested Citation

  • Benhamou, Eric, 2000. "Pricing convexity adjustment with Wiener chaos," LSE Research Online Documents on Economics 119104, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119104
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    File URL: http://eprints.lse.ac.uk/119104/
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    References listed on IDEAS

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    1. Vincent Lacoste, 1996. "Wiener Chaos: A New Approach To Option Hedging," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 197-213, April.
    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    3. Fabio Mercurio & Juan M. Moraleda, 1996. "A Family of Humped Volatility Structures," Tinbergen Institute Discussion Papers 96-169/2, Tinbergen Institute.
    4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Didier Kouokap Youmbi, 2012. "Yield to maturity modelling and a Monte Carlo Technique for pricing Derivatives on Constant Maturity Treasury (CMT) and Derivatives on forward Bonds," Papers 1204.4631, arXiv.org.
    2. 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.
    3. 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.
    4. Eric Benhamou, 2002. "A Martingale Result for Convexity Adjustment in the Black Pricing Model," Finance 0212005, University Library of Munich, Germany.
    5. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Cahiers de la Maison des Sciences Economiques b04050, Université Panthéon-Sorbonne (Paris 1).

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    More about this item

    Keywords

    Wiener chaos; Girsanov; convexity adjustment; CMS; lognormal zero-coupon bonds models;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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