Deep learning improves uncertainty and explanation in option pricing models
Uncertainty and Explainability in Deep Rough Volatility: A Neural Information-Theoretic Posterior Approach
Machine Learning
Summary
Financial markets often use complex mathematical models to price options, but it's hard to know how uncertain these prices are after using observed market data. The authors develop a new deep learning approach that not only estimates possible values of the model parameters but also quantifies the uncertainty of those estimates. They also introduce a method to explain which parts of the market data influence each parameter estimate. Their approach provides more reliable price estimates and clear insights about uncertainty for different types of financial contracts.
What this means in practice
- •For quantitative finance teams: Produce uncertainty-aware calibrations of rough volatility models to price complex financial derivatives more reliably.
- •For financial risk managers: Gain interpretable insights into which market data regions most influence parameter estimates and associated pricing uncertainty.
Authors
Damiano Brigo, Raphaël Huser, Dan Leonte
Abstract
Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not capture the uncertainty remaining after an implied-volatility (IV) surface has been observed. We develop a simulation-based inference framework for rough Heston (rHeston) calibration that learns the posterior distribution of the model parameters conditional on an IV surface. Using neural ratio estimation, we obtain calibrated posterior samples that can be propagated through heteroscedastic neural surrogate pricers for path-dependent exotic options. The resulting posterior-predictive distributions combine residual parameter uncertainty with conditional surrogate uncertainty and yield uncertainty-aware price intervals. We further introduce Hellinger-SHAP, an information-theoretic explainability method for posterior inference. Rather than attributing a single parameter point estimate, it applies local-background Kernel SHAP to a posterior-information functional measuring contraction from the prior to the posterior. This identifies maturity--moneyness regions associated with posterior information gain for individual rHeston parameters. In a simulation study, posterior-predictive intervals provide calibrated or conservative coverage across forward-start, barrier, and realized-variance claims, while point plug-in prices can be materially unreliable for selected contract regimes. Together, the UQ and XAI analyses provide a transparent framework for uncertainty-aware neural calibration and downstream exotic pricing under the specified prior-predictive model.