Stochastic processes are widely used for model building in the social, physical, engineering
and life sciences as well as in financial economics. In model building, statistical inference for …

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 …

The modeling of stochastic dependence is fundamental for understanding random systems
evolving in time. When measured through linear correlation, many of these systems exhibit a …

Using the large deviation principle (LDP) for a rescaled fractional Brownian motion B^H_t,
where the rate function is defined via the reproducing kernel Hilbert space, we compute …

Considering that both the entropy-based market information and the Hurst exponent are
useful tools for determining whether the efficient market hypothesis holds for a given asset …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …

Commodities are the most volatile markets, and forecasting their volatility is an issue of
paramount importance. We examine the dynamics of commodity markets volatility by …

We determine the amount of information contained in a time series of price returns at a given
time scale, by using a widespread tool of the information theory, namely the Shannon …

Mandelbrot and van Ness (1968) suggested fractional Brownian motion as a parsimonious
model for the dynamics of? nancial price data, which allows for dependence between …