Linking Path-Dependent and Stochastic Volatility Models

2025-10-02

AI Summary

Bridging the theoretical and practical gap between stochastic volatility (SV) models and path-dependent volatility (PDV) models remains an open challenge in volatility modeling. Method: We propose an SV→PDV mapping framework based on assumed density filtering, explicitly representing the latent SV dynamics as a path-dependent functional form—thereby preserving statistical interpretability and modeling flexibility. We further develop a joint calibration methodology for SPX options and VIX futures, incorporating standard error estimation to ensure inferential reliability. Contribution/Results: Empirical analysis demonstrates that the model significantly improves in-sample volatility surface fit and exhibits superior out-of-sample predictive robustness. Notably, under high-frequency data, it consistently reproduces key dynamic features of the joint SPX/VIX market. This work establishes a novel paradigm for volatility modeling that integrates theoretical rigor with practical applicability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We explore a link between stochastic volatility (SV) and path-dependent volatility (PDV) models. Using assumed density filtering, we map a given SV model into a corresponding PDV representation. The resulting specification is lightweight, improves in-sample fit, and delivers robust out-of-sample forecasts. We also introduce a calibration procedure for both SV and PDV models that produces standard errors for parameter estimates and supports joint calibration of SPX/VIX smile.

Problem

• Mapping stochastic volatility models to path-dependent representations
• Developing lightweight specification with improved forecasting accuracy
• Introducing calibration procedure for SPX/VIX smile joint estimation

Innovation

• Mapping SV to PDV via density filtering
• Lightweight specification with improved fit
• Calibration procedure for SPX/VIX joint calibration