On Errors and Bias of Fourier Transform Methods in Quadratic Term Structure Models

29 Pages Posted: 10 Jan 2006

See all articles by Nina Boyarchenko

Nina Boyarchenko

Federal Reserve Bank of New York

Sergei Levendorskii

Calico Science Consulting

Date Written: January 9, 2006

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 one is efficient for ATSMs of type $A_0(n)$ 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 Leippold and Wu (2002) 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.

Keywords: Derivative pricing, quadratic term structure models, Fourier transform, Fast Fourier transform

JEL Classification: C60, C69

Suggested Citation

Boyarchenko, Nina and Levendorskii, Sergei Z., On Errors and Bias of Fourier Transform Methods in Quadratic Term Structure Models (January 9, 2006). Available at SSRN: https://ssrn.com/abstract=874835 or http://dx.doi.org/10.2139/ssrn.874835

Nina Boyarchenko

Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States
212-720-7339 (Phone)
212-720-1582 (Fax)

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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