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We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…

Methodology · Statistics 2026-03-03 Qiang Liu , Zhi Liu , Wang Zhou

This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible…

Statistics Theory · Mathematics 2021-06-18 Phillip Murray , Riccardo Passeggeri , Almut E. D. Veraart , Mikko S. Pakkanen

We statistically analyse a multivariate HJM diffusion model with stochastic volatility. The volatility process of the first factor is left totally unspecified while the volatility of the second factor is the product of an unknown process…

Statistics Theory · Mathematics 2019-06-07 Olivier Féron , Pierre Gruet , Marc Hoffmann

We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…

Probability · Mathematics 2015-11-19 Enkelejd Hashorva , Mikhail Lifshits , Oleg Seleznjev

We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of…

Statistical Finance · Quantitative Finance 2008-12-02 Friedrich Hubalek , Petra Posedel

We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…

Machine Learning · Statistics 2024-05-17 Eunji Lim

Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…

Trading and Market Microstructure · Quantitative Finance 2019-08-14 Oleh Danyliv , Bruce Bland

Based on discrete observations, we develop a test to infer if the volatility function $\sigma(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = \sigma(t)dW_t$ is constant. The testing procedure is shown to be…

Statistics Theory · Mathematics 2026-04-29 Johannes Brutsche , Lukas Riepl

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…

Statistics Theory · Mathematics 2024-06-17 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

Statistics Theory · Mathematics 2015-03-19 Markus Bibinger , Markus Reiß

In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider $N$-dimensional Ito integrals with time varying matrix-valued…

Probability · Mathematics 2014-10-27 Claudio Heinrich , Mark Podolskij

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…

Mathematical Finance · Quantitative Finance 2023-05-09 Orcan Ogetbil , Narayan Ganesan , Bernhard Hientzsch

We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal…

Computational Finance · Quantitative Finance 2015-06-23 Matthew Lorig , Ronnie Sircar

We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…

Probability · Mathematics 2017-02-06 Hacène Djellout , Arnaud Guillin , Hui Jiang , Yacouba Samoura

We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…

Statistics Theory · Mathematics 2020-10-23 Gabor Lugosi , Shahar Mendelson

We derive a nonparametric test for constant beta over a fixed time interval from high-frequency observations of a bivariate \Ito semimartingale. Beta is defined as the ratio of the spot continuous covariation between an asset and a risk…

Statistics Theory · Mathematics 2015-02-20 Markus Reiß , Viktor Todorov , George Tauchen

We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency…

Statistics Theory · Mathematics 2009-09-07 Mathieu Rosenbaum

Even though the statistical theory of linear inverse problems is a well-studied topic, certain relevant cases remain open. Among these is the estimation of functions of bounded variation ($BV$), meaning $L^1$ functions on a $d$-dimensional…

Statistics Theory · Mathematics 2019-05-22 Miguel del Álamo , Axel Munk

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

Methodology · Statistics 2013-02-11 Cheng-Der Fuh , Huei-Wen Teng , Ren-Her Wang

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the…

Probability · Mathematics 2012-02-08 Amel Bentata , Rama Cont