Reduced-Order modeling for Heston stochastic volatility model

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Kozpinar S., UZUNCA M., KARASÖZEN B.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.53, no.6, pp.1515-1528, 2024 (SCI-Expanded) identifier identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.15672/hujms.1066143
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1515-1528
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.