Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility

Reza Mollapourasl (), Ali Fereshtian () and Michèle Vanmaele ()
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Reza Mollapourasl: Shahid Rajaee Teacher Training University
Ali Fereshtian: Shahid Rajaee Teacher Training University
Michèle Vanmaele: Ghent University

Computational Economics, 2019, vol. 53, issue 1, No 12, 259-287

Abstract: Abstract In this article, we price American options under Heston’s stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank–Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

Keywords: Radial basis function; Partition of unity; Operator splitting; American option pricing; Stochastic volatility; Heston’s model (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10614-017-9739-8

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