Volatility is rough
Event details
| Date | 04.11.2014 |
| Hour | 12:30 › 13:30 |
| Speaker | Mathieu ROSENBAUM (Ecole Polytechnique, Paris) |
| Location | |
| Category | Conferences - Seminars |
Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. We obtain that the regularity of the log-volatility corresponds to that of a fractional Brownian motion with Hurst exponent of H order 0.15. This leads us to model the log-volatility as a fractional Brownian motion with H<1/2; specifically we adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RSFV) to underline that, in contrast to FSV, H<1/2 and log-volatility behaves as fractional Brownian motion at all reasonable time scales. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it.
This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings. This is joint work with Jim Gatheral and Thibault Jaisson.
This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings. This is joint work with Jim Gatheral and Thibault Jaisson.
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