Reduced-Order Modeling for Heston Stochastic Volatility Model

TL;DR

This paper compares intrusive POD and data-driven DMD methods for reduced-order modeling of the Heston stochastic volatility model, highlighting trade-offs in accuracy and computational speed.

Contribution

It provides a comparative analysis of POD and DMD techniques applied to Heston's model, emphasizing the efficiency of DMD due to its non-intrusive approach.

Findings

DMD requires more modes than POD for similar accuracy

DMD achieves higher speed-up factors than POD

Both methods effectively model option pricing scenarios

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.