Robust High Precision Option Pricing By Fourier Transforms
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Robust High-Precision Option Pricing by Fourier Transforms
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.
Handbook of Computational Finance
Author: Jin-Chuan Duan
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-10-25
Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Mathematical Analysis and its Applications
This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.