Lord, Roger and Fang, Fang and Bervoets, Frank and Oosterlee, Kees (2007): A fast and accurate FFTbased method for pricing earlyexercise options under Lévy processes.

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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 wellknown riskneutral 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 exponentially Lévy models, including the exponentially affine jumpdiffusion models. For an Mtimes 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.
Item Type:  MPRA Paper 

Institution:  Rabobank International, Delft University of Technology and Center for Mathematics and Computer Science (CWI), Amsterdam 
Original Title:  A fast and accurate FFTbased method for pricing earlyexercise options under Lévy processes 
Language:  English 
Keywords:  Option pricing; Bermudan options; American options; convolution; Lévy Processes; Fast Fourier Transform 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing; Futures Pricing C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling 
Item ID:  1952 
Depositing User:  Roger Lord 
Date Deposited:  28. Feb 2007 
Last Modified:  17. Feb 2013 11:36 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/1952 