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 …

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

We present a neural network-based calibration method that performs the calibration task
within a few milliseconds for the full implied volatility surface. The framework is consistently …

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 …

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 …

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 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 …

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 …

How to reconcile the classical Heston model with its rough counterpart? We introduce a
lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but …

The passive and active motion of micron-sized tracer particles in crowded liquids and inside
living biological cells is ubiquitously characterised by'viscoelastic'anomalous diffusion, in …