Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

TL;DR

This paper develops reduced order models using proper orthogonal decomposition for efficiently pricing European and American options under complex stochastic volatility and jump-diffusion models, significantly speeding up computations.

Contribution

It introduces a ROM approach with POD for option pricing under advanced models, including American options with early exercise constraints, achieving substantial computational speedups.

Findings

ROMs are orders of magnitude faster than full order models.

The method accurately captures option prices across parameter variations.

Enforcing early exercise constraints via penalty improves American option pricing.

Abstract

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like 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.