Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications

TL;DR

This paper introduces SKINNs, a unified neural network framework that incorporates theoretical and domain insights as differentiable constraints, improving estimation and interpretability in finance applications.

Contribution

The paper presents SKINNs, a novel framework that embeds diverse insights into neural networks, enabling joint estimation of parameters with theoretical guarantees and improved financial modeling.

Findings

SKINNs improve out-of-sample option valuation and hedging performance.

SKINNs recover economically interpretable structural parameters with enhanced stability.

The framework provides consistency, asymptotic normality, and robustness under misspecification.

Abstract

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling. SKINNs define a class of M-estimators that are consistent and asymptotically normal with root-N convergence, sandwich covariance, and recovery of pseudo-true parameters under misspecification. We establish identification of structural parameters under joint flexibility, derive generalization and target-risk bounds under distributional shift in a convex proxy, and provide a restricted-optimal characterization of the weighting parameter that governs the bias-variance tradeoff. In an illustrative financial application to option pricing, SKINNs improve out-of-sample valuation and hedging performance, particularly at longer horizons and during high-volatility regimes, while recovering economically interpretable structural parameters with improved stability relative to conventional calibration. More broadly, SKINNs provide a general econometric framework for combining model-based reasoning with high-dimensional, data-driven estimation.