6533b826fe1ef96bd1285347

RESEARCH PRODUCT

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

Jari ToivanenJari ToivanenMaciej Balajewicz

subject

ta113Mathematical optimizationStochastic volatilityDiscretizationComputer scienceJump diffusionFinite difference method010103 numerical & computational mathematics01 natural sciencesNon-negative matrix factorization010101 applied mathematicsValuation of optionslinear complementary problemRange (statistics)General Earth and Planetary SciencesApplied mathematicsreduced order modelFinite difference methods for option pricing0101 mathematicsAmerican optionoption pricingGeneral Environmental Science

description

American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed

yearjournalcountryeditionlanguage
2016-01-01Procedia Computer Science
10.1016/j.procs.2016.05.360http://dx.doi.org/10.1016/j.procs.2016.05.360