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


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


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


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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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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