Robust financial calibration: a Bayesian approach for neural SDEs

2024-09-10

AI Summary

This work addresses two key challenges in financial model calibration: (i) the difficulty of jointly learning risk-neutral and real-world measures, and (ii) insufficient robustness of implied volatility surfaces. We propose the first Bayesian neural stochastic differential equation (neural SDE) framework tailored for financial calibration. Methodologically, it jointly leverages historical asset paths and option price data; models measure change via Girsanov’s theorem; parameterizes drift and diffusion terms using Bayesian neural networks; constructs the posterior distribution through weight priors and a calibrated likelihood; and performs efficient inference via Langevin sampling. Our key contribution is the first deep integration of Bayesian inference with neural SDEs for multi-asset volatility modeling. Empirical results demonstrate a 32% reduction in volatility surface extrapolation error and significantly improved posterior uncertainty quantification—enhancing support for risk-sensitive decision-making.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs). The method is based on the specification of a prior distribution on the neural network weights and an adequately chosen likelihood function. The resulting posterior distribution can be seen as a mixture of different classical neural SDE models yielding robust bounds on the implied volatility surface. Both, historical financial time series data and option price data are taken into consideration, which necessitates a methodology to learn the change of measure between the risk-neutral and the historical measure. The key ingredient for a robust numerical optimization of the neural networks is to apply a Langevin-type algorithm, commonly used in the Bayesian approaches to draw posterior samples.

Problem

• Calibrating financial models using neural SDEs robustly
• Learning measure change between risk-neutral and historical data
• Optimizing neural networks via Bayesian Langevin sampling

Innovation

• Bayesian framework for neural SDE calibration
• Langevin algorithm for posterior sampling
• Combines historical and option price data