Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation

TL;DR

This paper introduces a data-driven method to discover probabilistic laws from financial data using a novel stochastic SINDy approach under the risk-neutral measure, enabling prediction and data generation without ergodicity assumptions.

Contribution

The paper presents the first stochastic SINDy method formulated under the risk-neutral measure to recover BSDEs from limited financial data, bypassing ergodicity requirements.

Findings

Successfully recovers BSDEs from stock and option data.

Enables forward prediction and synthetic data generation.

Operates effectively with limited financial time series.

Abstract

In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability measure to recover the backward stochastic differential equation (BSDE) from a single pair of stock and option trajectories. Unlike existing approaches to identifying stochastic differential equations-which typically require ergodicity-our framework leverages the risk-neutral measure, thereby eliminating the ergodicity assumption and enabling BSDE recovery from limited financial time series data. Using this algorithm, we are able not only to make forward-looking predictions but also to generate new synthetic data paths consistent with the underlying probabilistic law.