6533b82afe1ef96bd128c2a5

RESEARCH PRODUCT

Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

Jari ToivanenJari ToivanenMaciej Balajewicz

subject

ta113Mathematical optimizationGeneral Computer ScienceStochastic volatilityDifferential equationEuropean optionMonte Carlo methods for option pricingJump diffusion010103 numerical & computational mathematics01 natural sciencesTheoretical Computer Science010101 applied mathematicsValuation of optionsModeling and Simulationlinear complementary problemRange (statistics)Asian optionreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingMathematics

description

Abstract 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.

yearjournalcountryeditionlanguage
2017-05-01Journal of Computational Science
10.1016/j.jocs.2017.01.004https://doi.org/10.1016/j.jocs.2017.01.004