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Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model

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

    (The African Institute of Financial Markets and Risk Management, University of Cape Town, Private Bag X3, Rondebosch, 7701, South Africa3Faculty of Economic and Financial Sciences, Department of Finance & Investment Management, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, South Africa)

Abstract

We provide efficient swaption volatility approximations for longer maturities and tenors under the lognormal forward-LIBOR model (LFM). In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the joint distribution of the forward rates is not known under a typical pricing measure, we resort to numerical discretization techniques. More specifically, we approximate the mean forward rates with a multi-dimensional weak order 2.0 Itō–Taylor scheme. The higher-order terms allow us to more accurately capture the state dependence in the drift terms and compute conditional expectations with second-order accuracy. We test our approximations for longer maturities and tenors using a quasi-Monte Carlo (QMC) study and find them to be substantially more effective when compared to the existing approximations, particularly for calibration purposes.

Suggested Citation

  • Jacques Van Appel & Thomas A. Mcwalter, 2018. "Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-26, June.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500206
    DOI: 10.1142/S0219024918500206
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    References listed on IDEAS

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