Linking Path-Dependent and Stochastic Volatility Models

Paper: arXiv 2510.02024

Authors: Samuel N. Cohen, Cephas Svosve

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical bridge between stochastic volatility (SV) and path-dependent volatility (PDV) models using Assumed Density Filtering (ADF). It presents rigorous stochastic calculus coupled with empirical applications to SPX/VIX options calibration, making it both mathematically sound and practical.

Research Flowchart

  flowchart TD
    A[Goal: Link Stochastic Volatility SV <br>to Path-Dependent Volatility PDV] --> B[Data Inputs: SPX & VIX Option Smiles]
    B --> C[Assumed Density Filtering ADF<br>Map SV to Lightweight PDV]
    C --> D[Joint Calibration Procedure<br>Compute Parameter Standard Errors]
    D --> E[Outcome: Improved In-Sample Fit &<br>Robust Out-of-Sample Forecasts]