RBF-PU method for pricing options under the jump–diffusion model with local volatility

RBF-PU method for pricing options under the jump–diffusion model with local volatility Meshfree methods based on radial basis functions (RBFs) are of general interest for solving partial differential equations (PDEs) because they can provide high order or spectral convergence for smooth solutions in complex geometries. For global RBF methods, one of the major disadvantages is the computational cost associated with the dense linear systems that arise. Therefore, this paper is currently directed toward localized RBF approximations known as the RBF partition of unity (RBF-PU) method for partial integro-differential equation (PIDE) arisen in option pricing problems in jump–diffusion model. RBF-PU method produces algebraic systems with sparse matrices which have small condition number. Also, for comparison, some stable time discretization schemes are combined with the operator splitting method to get a fully discrete problem. Numerical examples are presented to illustrate the convergence and stability of the proposed algorithms for pricing European and American options with Merton and Kou models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

RBF-PU method for pricing options under the jump–diffusion model with local volatility

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2018.01.002
Publisher site
See Article on Publisher Site

Abstract

Meshfree methods based on radial basis functions (RBFs) are of general interest for solving partial differential equations (PDEs) because they can provide high order or spectral convergence for smooth solutions in complex geometries. For global RBF methods, one of the major disadvantages is the computational cost associated with the dense linear systems that arise. Therefore, this paper is currently directed toward localized RBF approximations known as the RBF partition of unity (RBF-PU) method for partial integro-differential equation (PIDE) arisen in option pricing problems in jump–diffusion model. RBF-PU method produces algebraic systems with sparse matrices which have small condition number. Also, for comparison, some stable time discretization schemes are combined with the operator splitting method to get a fully discrete problem. Numerical examples are presented to illustrate the convergence and stability of the proposed algorithms for pricing European and American options with Merton and Kou models.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 1, 2018

References

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