Decoupling the Short- and Long-Term Behavior of Stochastic Volatility

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