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

Understand

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.