Meshfree Approximation for Multi-Asset Options

ICMA Centre Discussion Papers in Finance DP2009-07

22 Pages Posted: 28 Jun 2009

See all articles by Emmanuel Hanert

Emmanuel Hanert

Catholic University of Louvain (UCL)

Aanand Venkatramanan

University of Reading - ICMA Centre

Date Written: June 24, 2009

Abstract

We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.

Keywords: multi-asset options, radial basis function, meshfree approximation, collocation, multi-dimensional Levy process, basket options, PIDE, PDE

JEL Classification: C02, C3, G63

Suggested Citation

Hanert, Emmanuel and Venkatramanan, Aanand, Meshfree Approximation for Multi-Asset Options (June 24, 2009). ICMA Centre Discussion Papers in Finance DP2009-07, Available at SSRN: https://ssrn.com/abstract=1424987 or http://dx.doi.org/10.2139/ssrn.1424987

Emmanuel Hanert

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium

HOME PAGE: http://www.uclouvain.be/mila

Aanand Venkatramanan (Contact Author)

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom

HOME PAGE: http://www.icmacentre.ac.uk/index.php?id=146

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