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Analytical Approximation To Constant Maturity Swap Convexity Corrections In A Multi-Factor Sabr Model

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Listed:
  • BIN CHEN

    (MAS-2, Center for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

  • CORNELIS W. OOSTERLEE

    (MAS-2, Center for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

  • SACHA VAN WEEREN

    (Derivative Research and Validation Team, Rabobank International, Croeselaan 18, 3521 CB, Utrecht, The Netherlands)

Abstract

We consider the convexity correction in a multi-factor SABR type stochastic volatility model, in which the volatility and the short-term forward rate are modeled as independent factors. In general, the convexity correction is not analytically tractable in a multi-factor model, but based on the assumption of linear swap rates an analytic solution is available. Linear swap rate models are popular among practitioners for their efficiency and their ability to capture the swaption volatility smile. For an efficient approximation of the solution, we adopt the small disturbance asymptotics technique and construct a stochastic Taylor series of the underlying process. Several numerical experiments compare the accuracy of the approximation with a Monte Carlo benchmark solution.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:07:n:s0219024910006091
    DOI: 10.1142/S0219024910006091
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    References listed on IDEAS

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    1. Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
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