Hawkes (1971a, 1971b, 1972) introduced a family of models for stochastic point processes
called 'self-exciting and mutually exciting point processes' the essential property of which …

Estimating volatility from recent high frequency data, we revisit the question of the
smoothness of the volatility process. Our main result is that log-volatility behaves essentially …

From an analysis of the time series of realized variance using recent high-frequency data,
Gatheral et al.[Volatility is rough, 2014] previously showed that the logarithm of realized …

It has been recently shown that rough volatility models, where the volatility is driven by a
fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in …

Rough volatility models are known to reproduce the behavior of historical volatility data
while at the same time fitting the volatility surface remarkably well, with very few parameters …

We show that typical behaviors of market participants at the high frequency scale generate
leverage effect and rough volatility. To do so, we build a simple microscopic model for the …

Rough volatility models are very appealing because of their remarkable fit of both historical
and implied volatilities. However, due to the non-Markovian and nonsemimartingale nature …

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 …

We consider the joint SPX & VIX calibration within a general class of Gaussian polynomial
volatility models in which the volatility of the SPX is assumed to be a polynomial function of a …

This paper proposes to model and forecast realized volatility (RV) using the fractional
Ornstein–Uhlenbeck (fO–U) process with a general Hurst parameter, H. A two-stage method …