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 …

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 …

Techniques from deep learning play a more and more important role for the important task of
calibration of financial models. The pioneering paper by Hernandez [Risk, 2017] was a …

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 …

It has been recently shown that spot volatilities can be closely modeled by rough stochastic
volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian …

A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility.
First observed by Gatheral et al. in high‐frequency data, subsequently derived within market …

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a
power law with respect to the time to maturity. We construct a model of the underlying asset …

Rough volatility models are continuous time stochastic volatility models where the volatility
process is driven by a fractional Brownian motion with the Hurst parameter smaller than half …

We consider rough stochastic volatility models where the driving noise of volatility has
fractional scaling, in the 'rough'regime of Hurst parameter H< 1/2. This regime recently …

Statistical inference for rough volatility: Minimax theory Page 1 The Annals of Statistics 2024,
Vol. 52, No. 4, 1277–1306 https://doi.org/10.1214/23-AOS2343 © Institute of Mathematical …