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Linking Path-Dependent and Stochastic Volatility Models

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  • 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.

Suggested Citation

  • Samuel N. Cohen & Cephas Svosve, 2025. "Linking Path-Dependent and Stochastic Volatility Models," Papers 2510.02024, arXiv.org.
    • Handle: RePEc:arx:papers:2510.02024
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    References listed on IDEAS

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    1. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    2. Jakv{s}a Cvitani'c & Robert Liptser & Boris Rozovskii, 2006. "A filtering approach to tracking volatility from prices observed at random times," Papers math/0612212, arXiv.org.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    5. Florence Guillaume & Wim Schoutens, 2012. "Calibration risk: Illustrating the impact of calibration risk under the Heston model," Review of Derivatives Research, Springer, vol. 15(1), pages 57-79, April.
    6. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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