Reduced order models for pricing European and American options under stochastic volatility and jump-diffusion models

Maciej Balajewicz, Jari Toivanen

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)198-204
Number of pages7
JournalJournal of Computational Science
Volume20
DOIs
StatePublished - May 2017

Keywords

  • American option
  • European option
  • Linear complementary problem
  • Option pricing
  • Reduced order model

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Modeling and Simulation

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