Efficient Options Pricing Using the Fast Fourier Transform

Kwok, Yue Kuen; Leung, Kwai Sun; Wong, Hoi Ying

doi:10.1007/978-3-642-17254-0_21

Cited by 42 publications

(24 citation statements)

References 17 publications

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“…Next, we present a brief discussion of the use of the FFT techniques in the CONV method for pricing European options [refer to Lord et al (2008) and Kwok et al (2012) for details].…”

Section: Fft Technique and Conv Methodsmentioning

confidence: 99%

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Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes

Zheng¹,

Kwok²

2014

JCF

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We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous Lévy processes). Our numerical algorithms are non-trivial versions of the Fourier space time stepping method to nonlinear path dependent payoff structures, like those in variance products and volatility derivatives. The exotic path dependency associated with the discretely sampled realized variance is captured in the numerical procedure by updating two path dependent state variables across monitoring dates. The time stepping procedure between successive monitoring dates can be performed using fast Fourier transform calculations without the usual tedious time stepping calculations in typical finite difference algorithms. We also derive effective numerical procedures that compute the hedge parameters of variance products and volatility derivatives. Numerical tests on pricing various variance products and volatility derivatives were performed that illustrate efficiency, accuracy, reliability and robustness of the proposed Fourier transform algorithms.

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“…Next, we present a brief discussion of the use of the FFT techniques in the CONV method for pricing European options [refer to Lord et al (2008) and Kwok et al (2012) for details].…”

Section: Fft Technique and Conv Methodsmentioning

confidence: 99%

“…Lord et al (2008) and Jackson et al (2008) propose effective FFT algorithms for pricing derivatives with mild path dependence in the payoff structures, like the barrier options and American options. A recent review of various FFT algorithms in option pricing under Lévy processes can be found in Kwok et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes

Zheng¹,

Kwok²

2014

JCF

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“…Popular examples of such methods are finite difference methods (Gao et al, 2013;Huang & Oberman, 2013;Li et al, 2012;Meerschaert, 2004), finite element methods (Zhao & Lib, 2012), spectral methods (Bueno-Orovio et al, 2014;Huang et al, 2014), and other methods (Yan, 2013) for the forward equations describing anomalous diffusion etc. Further, such methods have been proposed for the backward equations in finance (Duquesne et al, 2010;Garreau & Kopriva, 2013;Kwok et al, 2012;Lee et al, 2012). In many of these methods, first, a time-evolution system of ordinary differential equations is derived from the given PIDE by the discretization of the spatial variable with finite differences, finite elements, polynomial expansions, etc., and some quadrature formulas.…”

Section: R\{0}mentioning

confidence: 99%

“…Then, the system is numerically solved using some numerical time integration methods such as second-order finite difference methods. In addition, in the case where the closed form of the characteristic function of the Lévy process can be obtained, methods based on the Fourier series or the Fourier transform are used in option pricing (Carr & Madan, 1999;Chourdakis, 2005;Fang & Oosterlee, 2008;Kwok et al, 2012).…”

Section: R\{0}mentioning

confidence: 99%

A fast and accurate numerical method for symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula

Tanaka¹

2015

IMA J Numer Anal

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In this paper, we propose a fast and accurate numerical method based on Fourier transform to solve Kolmogorov forward equations of symmetric scalar Lévy processes. The method is based on the accurate numerical formulas for Fourier transform proposed by Ooura. These formulas are combined with nonuniform fast Fourier transform (FFT) and fractional FFT to speed up the numerical computations. Moreover, we propose a formula for numerical indefinite integration on equispaced grids as a component of the method. The proposed integration formula is based on the sinc-Gauss sampling formula, which is a function approximation formula. This integration formula is also combined with the FFT. Therefore, all steps of the proposed method are executed using the FFT and its variants. The proposed method allows us to be free from some special treatments for a non-smooth initial condition and numerical time integration. The numerical solutions obtained by the proposed method appeared to be exponentially convergent on the interval if the corresponding exact solutions do not have sharp cusps. Furthermore, the real computational times are approximately consistent with the theoretical estimates.

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“…Duffie et al (2000) offered a comprehensive survey that Fourier transform methods are applicable to a wide range of stochastic processes, the class of exponential affine diffusions [e.g. see Kwok et al (2010) and Schmelzle (2010)]. Carr & Madan (1999) pioneered the use of the fast Fourier transform (FFT) technique by mapping the Fourier transform directly to option prices via the characteristic function.…”

Section: Introductionmentioning

confidence: 99%

Fourier Transform Methods for Option Pricing

Ding¹

2012

Fourier Transform Applications

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Efficient Options Pricing Using the Fast Fourier Transform

Cited by 42 publications

References 17 publications

Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes

Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes

A fast and accurate numerical method for symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula

Fourier Transform Methods for Option Pricing

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