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# The Finite Points Approximation to the PDE Problems in Multi-Asset Options

S. Vahdati1, D. Mirzaei2

Department of Mathematics, Faculty of Mathematics and Computer Science (Khansar), University of Isfahan, 81746-73441 Isfahan, Iran. E-mail: s.vahdati@khn.ui.ac.ir
Department of Mathematics, University of Isfahan, 81746-73441 Isfahan, Iran. E-mail: d.mirzaei@sci.ui.ac.ir

Computer Modeling in Engineering & Sciences 2015, 109-110(3), 247-262. https://doi.org/10.3970/cmes.2015.109.247

## Abstract

In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for single- and two-asset options are illustrated.

## Keywords

APA Style
Vahdati, S., Mirzaei, D. (2015). The finite points approximation to the PDE problems in multi-asset options. Computer Modeling in Engineering & Sciences, 109-110(3), 247-262. https://doi.org/10.3970/cmes.2015.109.247
Vancouver Style
Vahdati S, Mirzaei D. The finite points approximation to the PDE problems in multi-asset options. Comput Model Eng Sci. 2015;109-110(3):247-262 https://doi.org/10.3970/cmes.2015.109.247
IEEE Style
S. Vahdati and D. Mirzaei, "The Finite Points Approximation to the PDE Problems in Multi-Asset Options," Comput. Model. Eng. Sci., vol. 109-110, no. 3, pp. 247-262. 2015. https://doi.org/10.3970/cmes.2015.109.247

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