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.
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Notes
Boundary conditions in case of a call option, i.e. \(\xi =1\), can be found in Apel et al. (2001).
It is well-known that an American call option equals a European call option when the underlying asset pays no dividend.
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Acknowledgements
The first author would like to thank the Department of Applied Mathematics, Computer Science and Statistics of Ghent University and the FWO Scientific Research Network Stochastic Modelling with Applications in Financial Markets for some financial support during his scientific research stay at that department. The authors thank professor in ’t Hout for some fruitful discussion.
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Mollapourasl, R., Fereshtian, A. & Vanmaele, M. Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility. Comput Econ 53, 259–287 (2019). https://doi.org/10.1007/s10614-017-9739-8
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DOI: https://doi.org/10.1007/s10614-017-9739-8