The Finite Points Approximation to the PDE Problems in Multi-Asset Options
S. Vahdati and D. Mirzaei

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 109, No. 3, pp. 247-262, 2015
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Keywords Meshless methods, MLS approximation, finite points method, American options, Black-Scholes equation.

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.

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