Paper: arXiv 2511.08606

Authors: Qi Feng, Guang Lin, Purav Matlia, Denny Serdarevic

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper involves advanced stochastic calculus (Feynman-Kac, BSDEs, risk-neutral measures) and complex numerical methods (DNN-based PDE solving, stochastic SINDy, SR3), indicating high mathematical density. Empirical rigor is strong, with a detailed algorithmic workflow for both prediction and data generation using real-world financial data, though the lack of complete backtesting metrics keeps it from a perfect 10.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Discover BSDE underlying<br>Feynman-Kac formula"] --> B["Data Input:<br>Single pair of Stock<br>& Option trajectories"]
  B --> C["Core Methodology:<br>Data-driven Risk-Neutral<br>Stochastic SINDy"]
  C --> D["Computational Process:<br>Recover BSDE from<br>Limited Financial Data"]
  D --> E["Key Finding 1:<br>Forward Prediction<br>of derivative values"]
  D --> F["Key Finding 2:<br>Generation of synthetic<br>probabilistic law paths"]