ABSTRACT: In Gatheral et al. 2014, it has been shown that volatility exhibits a fractional behavior with a Hurst exponent $H < 0.5$, changing the typical perception of volatility. In their study, Gatheral and his co-authors used the realized volatility. In this analysis we explore the finding using two other estimators of spot volatility. The first set of estimators is known as range-based volatility estimators, and are calculated based on the open, close, high and low prices. We find that the log-volatility based on these estimators behaves like a fractional Brownian motion with $H$ lower than $0.1$. We also find that rough fractional stochastic volatility model (RFSV) is a relevant volatility model. Moreover, the prediction power of this model outperforms that of the AR, HAR and GARCH models in most cases. We revisit again this finding by studying implied volatility-based approximations of the spot volatility. Using at-the-money options on the S\&P500 index with short maturity, we are able to confirm that volatility is rough. The Hurst parameter found here, of order $0.3$, is slightly larger than that usually obtained from historical data. This is easily explained from a smoothing effect due to the remaining time to maturity of the considered options.
One paper can be found in the following link:
https://arxiv.org/abs/1702.02777
- Start date: 2020-02-04 11:00:00
- End date: 2020-02-04 12:30:00
- Venue: 1011 Evans Hall
- Address: 1011 Evans Hall, Berkeley, CA, 94720