Reduced-Order modeling for Heston stochastic volatility model

Kozpınar S., Uzunca M., Karasözen B.

Hacettepe Journal of Mathematics and Statistics, cilt.53, sa.6, ss.1515-1528, 2024 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 6
  • Basım Tarihi: 2024
  • Doi Numarası: 10.15672/hujms.1066143
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1515-1528
  • Anahtar Kelimeler: discontinuous Galerkin method, dynamic mode decomposition, Heston model, option pricing, proper orthogonal decomposition, reduced-order modeling
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Hes-ton’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.