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A numerical study of radial basis function based methods for option pricing under one dimension jump-diffusion model

Chan, Ron T.L. and Hubbert, Simon (2010) A numerical study of radial basis function based methods for option pricing under one dimension jump-diffusion model. Applied Numerical Mathematics , ISSN 0168-9274. (Submitted)

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Official URL: http://www.sciencedirect.com/science/journal/01689...

Abstract

The aim of this paper is to show how option prices in the Jump-diffusion model can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the Ameri- can put and the European vanilla call/put options on dividend-paying stocks in the Merton and Kou Jump-diffusion models. The radial basis function we select is the Cubic Spline. We also propose a simple numerical algorithm for finding a finite computational range of a global integral term in the PIDE so that the accuracy of approximation of the integral can be improved. Moreover, the solution functions of the PIDE are approximated explicitly by RBFs which have exact forms so we can easily compute the global intergal by any kind of numerical quadrature. Finally, we will also show numerically that our scheme is second order accurate in spatial variables in both American and European cases.

Item Type: Article
Additional Information: This is a pre-print of an article submitted to Applied Numerical Mathematics
Keyword(s) / Subject(s): Levy processes, the jump-diffusion model, partial-integro differential equation, radial basis function, cubic spline, european option, american option
School or Research Centre: Birkbeck Schools and Research Centres > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
Depositing User: Mr Ron Chan
Date Deposited: 26 Nov 2010 09:17
Last Modified: 09 Sep 2013 10:19
URI: http://eprints.bbk.ac.uk/id/eprint/2871

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