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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 as a fractional… (More)

We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency $1/\Delta_n$, with $\Delta_n$ going to zero. The goal of this paper is to provide an estimator for the… (More)

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 order to… (More)

We consider the regression model with observation error in the design: y = Xµ ⁄ + »; Z = X + ¥: Here the random vector y 2R n and the random n£p matrix Z are observed, the n £ p matrix X is unknown,… (More)

on the basis of their commonly known strength levels, and privately observed strengthshocks

Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the… (More)

We consider the model y - Y0 +, Z- X + 3? where the random vector y ∈ ℝ n and the random n × p matrix Z are observed, the n x p matrix X is unknown, Θ is an n x p random noise matrix, ξ ∈ ℝ n is a… (More)

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. However,… (More)

In this work, we provide a framework linking microstructural properties of an asset to the tick value of the exchange. In particular, we bring to light a quantity, referred to as implicit spread,… (More)

In this paper, we provide a model which accommodates the assumption of a continuous efficient price with the inherent properties of ultra-high-frequency transaction data (price discreteness,… (More)