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EFFICIENT LONG-DATED SWAPTION VOLATILITY APPROXIMATION IN THE FORWARD-LIBOR MODEL

Jacques van Appel () and Thomas A. McWalter
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 04, 1-26

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.

Keywords: LIBOR model; swaption; volatility approximation; efficient calibration (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500206

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