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Moment Approximations Of Displaced Forward-Libor Rates With Application To Swaptions

Author

Listed:
  • JACQUES VAN APPEL

    (Faculty of Science, Department of Statistics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa)

  • THOMAS A. MCWALTER

    (Faculty of Science, Department of Statistics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa†The African Institute of Financial Markets and Risk Management, University of Cape Town, Private Bag X3, Rondebosch, 7701, South Africa)

Abstract

We present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito–Taylor expansion in combination with a second-order Delta method. This more accurately accounts for state dependence in the drift terms, improving upon previous approaches. To verify this improvement we conduct quasi-Monte Carlo simulations. We use the new mean approximation to provide an improved swaption volatility approximation, and compare this to the approaches of Rebonato, Hull–White and Kawai, adapted to price swaptions under the DLFM. Rebonato and Hull–White are found to be the least accurate. While Kawai is the most accurate, it is computationally inefficient. Numerical results show that our approach strikes a balance between accuracy and efficiency.

Suggested Citation

  • Jacques Van Appel & Thomas A. Mcwalter, 2020. "Moment Approximations Of Displaced Forward-Libor Rates With Application To Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-29, November.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:07:n:s0219024920500466
    DOI: 10.1142/S0219024920500466
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