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 …

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 …

We introduce affine Volterra processes, defined as solutions of certain stochastic
convolution equations with affine coefficients. Classical affine diffusions constitute a special …

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 …

In this paper, we present a comprehensive survey of continuous stochastic volatility models,
discussing their historical development and the key stylized facts that have driven the field …

We develop a statistical theory for a continuous time approximately log‐normal fractional
stochastic volatility model to examine whether the volatility is rough, that is, whether the …

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging
problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may …

Rough volatility models are recently popularized by the need of a consistent model for the
observed empirical volatility in the financial market. In this case, it has been shown that the …

We conduct an empirical analysis of rough and classical stochastic volatility models to the
SPX and VIX options markets. Our analysis focusses primarily on calibration quality and is …