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On Errors And Bias Of Fourier Transform Methods In Quadratic Term Structure Models

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Author Info

  • NINA BOYARCHENKO

    (The University of Chicago Graduate School of Business, 5807 South Woodlawn Avenue, Chicago, IL 60637, USA)

  • SERGEI LEVENDORSKIǏ

    ()
    (Department of Economics, The University of Texas at Austin, 1 University Station C3100, Austin, TX 78712-0301, USA)

Abstract

We analyze and compare the performance of the Fourier transform method in affine and quadratic term structure models. We explain why the method of the reduction to FFT in dimension 1 is efficient for ATSMs of type A0(n), but may lead to sizable errors for QTSMs unless computational errors are taken into account properly. We suggest a certain improvement and generalization which make FFT more accurate and, for the same precision, faster than the Leippold and Wu [M. Leippold and L. Wu, Option pricing under the quadratic class, Journal of Financial and Quantitative Analysis 37(2) (2002) 271–295] method. We deduce simple general recommendations for the choice of parameters of computational schemes for QTSMs, which ensure a given precision, and an approximate formula for the bias which FFT produces.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 10 (2007)
Issue (Month): 02 ()
Pages: 273-306

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Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:02:p:273-306

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Related research

Keywords: Derivative pricing; quadratic term structure models; Fourier transform; fast Fourier transform;

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Cited by:
  1. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
  2. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.

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