We learn from data that volatility is mostly path-dependent: up to 90% of the variance of the
implied volatility of equity indexes is explained endogenously by past index returns, and up …

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 …

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 …

We consider a stochastic volatility model where the dynamics of the volatility are described
by linear functions of the (time extended) signature of a primary underlying process, which is …

The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the
volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck …

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic
volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact …

Since VIX options started trading in 2006, many researchers have tried to build a model that
jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures and VIX …

The rough Bergomi model introduced by Bayer et al.[Quant. Finance, 2015, 1–18] has been
outperforming conventional Markovian stochastic volatility models by reproducing implied …