Reduced-Order modeling for Heston stochastic volatility model

Year 2024, Volume: 53 Issue: 6, 1515 - 1528, 28.12.2024

Sinem Kozpınar , Murat Uzunca , Bülent Karasözen

https://doi.org/10.15672/hujms.1066143

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.

Keywords

option pricing, Heston model, discontinuous Galerkin method, reduced order modeling, proper orthogonal decomposition, dynamic mode decomposition

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