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 …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …

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 …

We introduce the notion of rough local stochastic volatility models, extending the classical
concept to the case where volatility is driven by some Volterra process. In this setting, we …

We consider a fractional version of the Heston volatility model which is inspired by [H.
Guennoun et al., SIAM J. Financial Math,, 9 (2018), pp. 1017--1045]. Within this model we …

We develop a method to study the implied volatility of exotic underlyings, with special focus
on volatility derivatives such as VIX options. Remarkably, our approach is flexible enough to …

We construct a deep learning-based numerical algorithm to solve path-dependent partial
differential equations arising in the context of rough volatility. Our approach is based on …

The class of Affine (Jump) Diffusion (AD) has, due to its closed form characteristic function
(ChF), gained tremendous popularity among practitioners and researchers. However, there …

We provide explicit small-time formulae for the at-the-money implied volatility, skew and
curvature in a large class of models, including rough volatility models and their multi-factor …

We study Euler-type discrete-time schemes for the rough Heston model, which can be
described by a stochastic Volterra equation (with non-Lipschitz coefficient functions) or by an …