Statistical inference for rough volatility: Minimax theory
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 …
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
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 …
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
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 …
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 …
Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes …
The Fine Structure of Volatility Dynamics
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 …
standard semimartingale process, with paths of finite quadratic variation, or a rough process …
A nonparametric test for rough volatility
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 …
standard semimartingale process, with paths of finite quadratic variation, or a rough process …
Rate-optimal estimation of mixed semimartingales
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 …
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 …
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 …
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 …
controlled by fractional Brownian motions with Hurst parameter H≤ 1∕ 2. We show that the …