Structured neural solvers improve pricing accuracy for complex financial models

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

Machine LearningComputational Engineering, Finance, and Science

Summary

Pricing financial options accurately involves solving complex mathematical equations that describe how prices change over time with uncertainty. The authors developed a new kind of neural network, called BeTINN, which better captures how these equations behave across many different scenarios. Their method improves accuracy not only in predicting option prices but also in important related quantities that traders use to manage risk. They also found that checking just the overall prediction quality isn't enough; you need to look carefully at how well the network predicts detailed changes too. This work helps make advanced financial modeling faster and more reliable.

What this means in practice

  • For financial modelers: Improve accuracy and efficiency of option pricing models involving stochastic volatility using structured neural solvers.
  • For risk management teams: Generate more reliable sensitivity metrics (Greeks) from complex financial PDEs for better hedging strategies.

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.
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