A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes

23 Pages Posted: 28 Feb 2007

See all articles by Roger Lord

Roger Lord

Cardano Risk Management

Fang Fang

Delft University of Technology

Frank Bervoets

Rabobank International, London Branch

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: February 27, 2007

Abstract

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognising that it is a convolution. The resulting convolution is dealt with numerically by using the Fast Fourier Transform (FFT). This novel pricing method, which we dub the Convolution method, CONV for short, is applicable to a wide variety of payoffs and only requires the knowledge of the characteristic function of the model. As such the method is applicable within exponential Lévy models, including the exponentially affine jump-diffusion models. For an M-times exercisable Bermudan option, the overall complexity is O(MN log(N)) with N grid points used to discretise the price of the underlying asset. It is shown how to price American options efficiently by applying Richardson extrapolation to the prices of Bermudan options.

Keywords: Option pricing , Bermudan options, American options, convolution, Lévy processes, Fast Fourier Transform

JEL Classification: C63, G13

Suggested Citation

Lord, Roger and Fang, Fang and Bervoets, Frank and Oosterlee, Cornelis W., A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes (February 27, 2007). Available at SSRN: https://ssrn.com/abstract=966046 or http://dx.doi.org/10.2139/ssrn.966046

Roger Lord (Contact Author)

Cardano Risk Management ( email )

Rotterdam 3011 AA
Netherlands

Fang Fang

Delft University of Technology ( email )

Stevinweg 1
Stevinweg 1
Delft, 2628 CN
Netherlands

Frank Bervoets

Rabobank International, London Branch ( email )

Thames Court
1 Queenhithe
London EC 4V 3RL
United Kingdom

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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