Statistical inference for rough volatility: Minimax theory

CH Chong, M Hoffmann, Y Liu… - The Annals of …, 2024 - projecteuclid.org
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 …

Convergence of heavy-tailed Hawkes processes and the microstructure of rough volatility

U Horst, W Xu, R Zhang - arXiv preprint arXiv:2312.08784, 2023 - arxiv.org
We establish the weak convergence of the intensity of a nearly-unstable Hawkes process
with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market …

Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance

X Han, A Schied - arXiv preprint arXiv:2307.02582, 2023 - arxiv.org
We consider the problem of estimating the roughness of the volatility in a stochastic volatility
model that arises as a nonlinear function of fractional Brownian motion with drift. To this end …

The multivariate fractional Ornstein-Uhlenbeck process

R Dugo, G Giorgio, P Pigato - arXiv preprint arXiv:2408.03051, 2024 - arxiv.org
Starting from the notion of multivariate fractional Brownian Motion introduced in [F.
Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes …

The Fine Structure of Volatility Dynamics

CH Chong, V Todorov - Available at SSRN 4660138, 2023 - papers.ssrn.com
We develop a nonparametric test for deciding whether volatility of an asset follows a
standard semimartingale process, with paths of finite quadratic variation, or a rough process …

A nonparametric test for rough volatility

CH Chong, V Todorov - arXiv preprint arXiv:2407.10659, 2024 - arxiv.org
We develop a nonparametric test for deciding whether volatility of an asset follows a
standard semimartingale process, with paths of finite quadratic variation, or a rough process …

Rate-optimal estimation of mixed semimartingales

CH Chong, T Delerue, F Mies - arXiv preprint arXiv:2207.10464, 2022 - arxiv.org
Consider the sum $ Y= B+ B (H) $ of a Brownian motion $ B $ and an independent fractional
Brownian motion $ B (H) $ with Hurst parameter $ H\in (0, 1) $. Even though $ B (H) $ is not …

When frictions are fractional: Rough noise in high-frequency data

CH Chong, T Delerue, G Li - Journal of the American Statistical …, 2024 - Taylor & Francis
The analysis of high-frequency financial data is often impeded by the presence of noise.
This article is motivated by intraday return data in which market microstructure noise …

Path-dependent PDEs for volatility derivatives

A Pannier - arXiv preprint arXiv:2311.08289, 2023 - arxiv.org
We regard options on VIX and Realised Variance as solutions to path-dependent PDEs in a
continuous stochastic volatility model. The modeling assumption specifies that the …

Power variations and limit theorems for stochastic processes controlled by fractional Brownian motions

Y Liu, X Wang - Electronic Journal of Probability, 2024 - projecteuclid.org
In this paper we establish limit theorems for power variations of stochastic processes
controlled by fractional Brownian motions with Hurst parameter H≤ 1∕ 2. We show that the …