Volatility forecast with the regularity modifications

Abstract

The promising empirical results presented using high-frequency data show that the log-volatility behaves essentially as a fractional Brownian motion (fBm) with a Hurst exponent smaller than 0.5. Motivated by these findings, we propose the autoregressive rough volatility (ARRV) model, which combines the fractional Gaussian noise (fGn) process and time series models to forecast volatility. We apply this model to the VIX index by adopting the fBm approximation technique, and our results indicate that the ARRV model can significantly improve VIX out-of-sample forecast accuracy, particularly during turbulent times.