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Cms, Cms Spreads And Similar Options In The Multi-Factor Hjm Framework

Author

Listed:
  • PIERRE HANTON

    (BNP Paribas Fortis, Model Validation, Belgium)

  • MARC HENRARD

    (OpenGamma, Quantitative Research, United Kingdom)

Abstract

Constant maturity swaps (CMS) and CMS spread options are analysed in the multi-factor HJM framework. For Gaussian models, which include a version of the Libor Market Models and the G2++ model, explicit approximated pricing formulae are provided. Two approximating approaches are proposed: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach borrows from previous literature on other models; the second approach is new. For the latter, the price approximation errors are smaller than in the previous literature and negligible in practice. These approaches are being used here to price standard CMS and CMS spreads and can be used for other European exotic products.

Suggested Citation

  • Pierre Hanton & Marc Henrard, 2012. "Cms, Cms Spreads And Similar Options In The Multi-Factor Hjm Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-18.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:07:n:s0219024912500483
    DOI: 10.1142/S0219024912500483
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    Cited by:

    1. Parviz Rakhmonov & Firuz Rakhmonov, 2022. "CMS spread options in quadratic Gaussian model," Review of Derivatives Research, Springer, vol. 25(3), pages 283-291, October.

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