Linking Path-Dependent and Stochastic Volatility Models

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.