Physics-Informed Koopman Neural Estimation of the Heston Model from High-Frequency Observations

Abstract

We propose a physics-informed learning framework, called Koopman-PINN, to estimate the parameters of the Heston stochastic volatility model with high-frequency price data in financial markets. The method integrates a nonparametric volatility estimation (known as ART-filter in the literature), moment-based parameter initialization, and a neural Koopman operator constrained by the infinitesimal generator of the underlying stochastic differential equation. By incorporating a generator-based loss, the model bridges Koopman theory and neural modeling to handle partially observed coupled stochastic dynamics in a manner consistent with continuous-time evolution. Across diverse parameter combinations reflecting varying market conditions, Koopman-PINN consistently achieves accurate and robust five-parameter recovery, outperforming existing estimators under a minimal set of initialization assumptions.