Abstract
In this work, we apply the local Wendland radial basis function (RBF) for solving the time-dependent multi dimensional option pricing nonlinear PDEs. Firstly, cross derivative terms of the PDE are removed with a change of spatial variables based in LDLT factorization of the diffusion matrix. Then, it is discussed that the valuation of a multi-asset option up to 4D can be computed using a modified shape parameter algorithm. In fact, several experiments containing of three and four assets are worked out showing that the results of the presented method are in good agreement with the literature and could be much more accurate once the shape parameter is chosen carefully.
Highlights
Multi-dimensional option pricing problems are frequent in the industry related to real markets
The aim of this paper is to introduce in the radial basis function (RBF) method, some strategies to improve the competitiveness allowing the resolution of four spatial dimensional option pricing problems unlike the recent pessimistic forecast of prestigious practitioners of the method [13, p. 160]
The graph shows an stable behavior of RBF application for pricing multi-dimensional problems
Summary
Multi-dimensional option pricing problems are frequent in the industry related to real markets. After the 2008 financial crisis such as regulation, fiscal issues, Copyright c 2018 The Author(s). Soleymani capitalization costs and currencies’ volatilities, the number of exotic options sold has reduced. The demand of competitive and reliable numerical methods for solving multidimensional problems (arising from related models) continues claiming the attention of academia
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