Decoupling the short- and long-term behavior of stochastic volatility

TL;DR

This paper introduces a novel continuous-time stochastic volatility model that captures both roughness and long memory, improving volatility forecasting accuracy across diverse assets.

Contribution

The paper presents a new class of models based on Brownian semistationary processes that incorporate both roughness and long memory in volatility modeling.

Findings

Models fit realized volatility data well, showing roughness and persistence.

Proposed models outperform benchmarks in volatility forecasting.

Evidence supports the coexistence of roughness and long memory in volatility.

Abstract

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized facts often found in volatility data. Our prime model is based on the so-called Brownian semistationary process and we derive a number of theoretical properties of this process, relevant to volatility modeling. Applying the models to realized volatility measures covering a vast panel of assets, we find evidence consistent with the hypothesis that time series of realized measures of volatility are both rough and very persistent. Lastly, we illustrate the utility of the models in an extensive forecasting study; we find that the models proposed in this paper outperform a wide array of benchmarks considerably, indicating that it pays off to exploit both roughness and persistence in volatility forecasting.