Robust High-Precision Option Pricing by Fourier Transforms: Contour Deformations and Double-Exponential Quadrature
33 Pages Posted: 25 Aug 2018 Last revised: 13 Nov 2018
Date Written: April 30, 2018
While the idea of pricing options by Fourier methods has been around for more than two decades, the numerical evaluation of the necessary semi-infinite Fourier style integrals remains a challenging problem. Existing methods in the literature frequently lack robustness, and in practice often result in disappointing precision, especially when the integrands become oscillatory or poorly dampened. In this paper we propose two new methods to evaluate these integrals, both relying on double-exponential quadrature. In the first, we use a carefully constructed contour deformation to dampen out Fourier oscillations in the integrand, followed by an application of either automatic or fixed-size double exponential quadrature. In the second, we use a node-placement trick by T. Ooura to ensure that the integrand decays double-exponentially at all node points, even in the presence of oscillations. While both methods are generally applicable, for concreteness we mostly frame our development in the context of the popular (and tricky) Heston stochastic volatility model. As demonstrated by tests on hundred thousands of challenging model and option parameter configurations, our two schemes are efficient, accurate, and robust, and significantly outperform standard methods. For instance, in a challenging bulk test our recommended scheme is on average about 10 orders of magnitude more precise than standard adaptive Gauss-Lobatto quadrature, and is also far more robust.
Keywords: Option Pricing, Fourier Methods, Contour Deformation, Heston Model, Double-Exponential Rule
JEL Classification: C63, G12, G13
Suggested Citation: Suggested Citation