Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
Balajewicz, M., & Toivanen, J. (2017). Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models. Journal of Computational Science, 20, 198-204. https://doi.org/10.1016/j.jocs.2017.01.004
Published inJournal of Computational Science
© 2017 Elsevier B.V. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range.
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