ON ERRORS AND BIAS OF FOURIER TRANSFORM METHODS IN QUADRATIC TERM STRUCTURE MODELS

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 Analysis37(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.