Journal
APPLIED NUMERICAL MATHEMATICS
Volume 110, Issue -, Pages 159-173Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2016.08.006
Keywords
Radial basis function; Finite difference; Option pricing; Jump-diffusion models; Partial integro-differential equation
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Funding
- Council of Scientific and Industrial Research, India [10-2(5)/2007(ii)-E.U.II, 09/092(0715)/2009-EMR-I]
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In this article, we present a radial basis function based implicit explicit numerical method to solve the partial integro-differential equation which describes the nature of the option price under jump diffusion model. The governing equation is time semi discrtized by using the implicit-explicit backward difference method of order two (IMEX-BDF2) followed by radial basis function based finite difference (RBF-FD) method. The numerical scheme derived for European option is extended for American option by using operator splitting method. Numerical results for put and call option under Merton and Kou models are given to illustrate the efficiency and accuracy of the present method. The stability of time semi discretized scheme is also proved. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.
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