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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 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 exponentially Lévy models, including the exponentially affine jump-diffusion models. Foran M-times exercisable Bermudan option, the overall complexity is OMN logN 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 FFT-based method for pricing early-exercise 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 PricingC - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling-





Autor: Lord, Roger

Fuente: https://mpra.ub.uni-muenchen.de/1952/







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