Minerva Investment Management Society

Quantitative Research Paper

Path Dependent Volatility Model

· Quantitative Research

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Summary

The Quantitative Research Division is pleased to present our latest study: “Path-Dependent Volatility Models: Theoretical and Empirical Evidence.”

This project examines one of the most fundamental questions in modern volatility modelling: Can implied volatility be explained endogenously from the past returns of the underlying index, without relying on an independent stochastic volatility process?

The report contains the full theoretical framework of Path-Dependent Volatility models in both discrete and continuous time, introduces a Markovian approximation suitable for simulation and option pricing, and evaluates the model empirically using more than two decades of SPX and VIX data.

Our findings show that the PDV model explains nearly 87% of the out-of-sample variation in implied volatility using only past SPX returns. The framework reproduces major volatility spikes, displays robust statistical behaviour, and uncovers a low-dimensional structure underlying implied volatility dynamics.

Beyond forecasting, we also highlight how PDV can be embedded into option pricing methodologies and jointly calibrated to SPX and VIX derivatives.

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Details

Published
11 December 2025
Division
Quantitative Research
Type
Quantitative Research Paper
Pages
22
Authors
3

Cite this report

Minerva Investment Management Society (2025). Path Dependent Volatility Model. Quantitative Research. https://minervaims.org/archive/path-dependent-volatility-model-2025

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