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

Battle Count: 73

Highly relevant to quantitative trading, particularly in options trading and derivatives pricing. The framework enables: (1) online prediction of option prices from a single stock-option trajectory pair without assuming a known model; (2) discovery of the underlying BSDE dynamics directly from market data; (3) generation of synthetic stock-option paths for backtesting strategies. The risk-neutral measure formulation is directly applicable to derivatives pricing. However, practical deployment would require addressing the limitations around non-trading intervals, quantitative validation, and computational efficiency for real-time trading.

High complexity due to the multi-step pipeline: (1) DNN training with physics-informed loss and LBFGS optimization; (2) SINDy-based diffusion coefficient estimation; (3) Brownian increment extraction; (4) Stochastic SINDy with SR3 for BSDE discovery; (5) Online prediction with sliding memory window and iterative retraining; (6) Monte Carlo simulation for data generation. Requires expertise in stochastic calculus, PDE theory, sparse regression, and deep learning. The interplay between DNN retraining and SINDy rediscovery at each prediction step adds significant computational overhead.

The algorithm is described in detail with five clear steps, mathematical formulations, and hyperparameter structure. However, no code repository is provided, specific hyperparameter values (α, γ, δ, τ) are not fully disclosed, and results are presented only in figures without quantitative error tables. The Black-Scholes benchmark is reproducible analytically, and Apple data is publicly available, but the exact DNN architecture and training details are not fully specified.