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 …

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 …

The quadratic rough Heston model provides a natural way to encode Zumbach effect in the
rough volatility paradigm. We apply multi-factor approximation and use deep learning …

Differential machine learning combines automatic adjoint differentiation (AAD) with modern
machine learning (ML) in the context of risk management of financial Derivatives. We …

This paper presents new machine learning approaches to approximate the solutions of
optimal stopping problems. The key idea of these methods is to use neural networks, where …

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 …