Beyond Time Induction: Structured Conditional Neural Solvers for Parametric Stochastic-Volatility Pricing

Paper: arXiv 2610.19254

Authors: Jose Miguel Lara Rangel, Mixtli Vazquez Mendoza

Abstract

Physics-informed neural networks provide a flexible framework for learning parametric PDE solution families without labeled data, yet preserving accurate derivatives across heterogeneous regimes remains challenging. Structured neural solvers offer compact representations, but restrictive conditional parameterizations can limit adaptation across the solution family. We introduce BeTINN, a structured conditional architecture extending time-induced modulation through multi-directional time-parameter conditioning and a joint residual pathway. We evaluate BeTINN on the Heston stochastic-volatility PDE, a demanding parametric problem with mixed derivatives and economically relevant first- and second-order sensitivities. BeTINN improves joint accuracy across normalized option value and key sensitivity metrics relative to our baselines. Controlled ablations characterize the roles of its architectural components. We further find that validation physics loss is informative but does not fully determine differential fidelity, and that accurate solution values can coexist with localized derivative errors. These results support structured conditional adaptation and motivate derivative-aware evaluation when sensitivities are downstream quantities of interest.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel neural network architecture for solving parametric PDEs in finance, specifically the Heston model. It demonstrates strong mathematical foundations and a solid empirical evaluation of its performance against baselines, focusing on both solution accuracy and derivative fidelity. The work is innovative in its approach to conditional adaptation for neural solvers.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Parametric PDE Solving with PINNs] --> B{Methodology: BeTINN Architecture};
    B --> C[Inputs: Heston Stochastic-Volatility PDE & Parameters];
    C --> D{Computational Process: Training & Evaluation of BeTINN};
    D --> E[Outcome 1: Improved Joint Accuracy in Option Value & Sensitivities];
    D --> F[Outcome 2: Validation Physics Loss ≠ Full Derivative Fidelity];
    D --> G[Outcome 3: Accurate Values can Coexist with Localized Derivative Errors];