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Markus Bibinger

Publications and source records attributed to Markus Bibinger.

At least 19 recordsLinked to original sources
arXiv2026

Asset-specific limit order microstructure noise: Parameter estimation and empirical evidence

The one-sided microstructure noise model for high-frequency quotes from a limit order book is generalized to capture asset-specific noise tail behaviour. Estimation of a noise tail parameter becomes the key step for inference. This is possible based on moments of the high-frequency returns when specifying a parametric noise model. For a Gamma noise distribution, we establish a central limit theorem for 1-dependent observations from the resulting Gamma difference distribution and prove that it is valid also in the convolution model with general semimartingale log-price dynamics. We highlight that the noise tail parameter has important implications for estimating the efficient price and its volatility. An empirical analysis of recent NASDAQ limit order book data demonstrates that asset-specific noise tail parameters are relevant in practice.

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arXiv2025

Modeling and Forecasting Realized Volatility with Multivariate Fractional Brownian Motion

A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility (RV). We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel method to estimate model parameters, establishing its consistency and asymptotic normality. Additionally, we develop a time-reversibility test, which is typically not rejected by RV data. When the data generating process is a time-reversible mfBm, we derive optimal forecasting formulae and analyze their properties. A key insight is that an mfBm with different Hurst exponents and non-zero correlations can reduce forecasting errors compared to a one-dimensional model. Consistent with this theory, out-of-sample forecasts using the time-reversible mfBm show improvements over univariate fBm, particularly when the estimated Hurst exponents differ significantly. Empirical results demonstrate that mfBm outperforms HAR and its variants in terms of out-of-sample forecast.

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arXiv2024

Probabilistic models and statistics for electronic financial markets in the digital age

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the R\'{e}nyi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.

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arXiv2024

Jump detection in high-frequency order prices

We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we consider one-sided microstructure noise for order prices in a limit order book. We develop methods to estimate, locate and test for jumps using local minima of best ask quotes. We provide a local jump test and show that we can consistently estimate jump sizes and jump times. One main contribution is a global test for jumps. We establish the asymptotic properties and optimality of this test. We derive the asymptotic distribution of a maximum statistic under the null hypothesis of no jumps based on extreme value theory. We prove consistency under the alternative hypothesis. The rate of convergence for local alternatives is determined and shown to be much faster than optimal rates for the standard market microstructure noise model. This allows the identification of smaller jumps. In the process, we establish uniform consistency for spot volatility estimation under one-sided noise. Online jump detection based on the new approach is shown to achieve a speed advantage compared to standard methods applied to mid quotes. A simulation study sheds light on the finite-sample implementation and properties of the new approach and draws a comparison to a popular method for market microstructure noise. We showcase how our new approach helps to improve jump detection in an empirical analysis of intra-daily limit order book data.

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arXiv2023

Testing for jumps in processes with integral fractional part and jump-robust inference on the Hurst exponent

We develop and investigate a test for jumps based on high-frequency observations of a fractional process with an additive jump component. The Hurst exponent of the fractional process is unknown. The asymptotic theory under infill asymptotics builds upon extreme value theory for weakly dependent, stationary time series and extends techniques for the semimartingale case from the literature. It is shown that the statistic on which the test is based on weakly converges to a Gumbel distribution under the null hypothesis of no jumps. We prove consistency under the alternative hypothesis when there are jumps. Moreover, we establish convergence rates for local alternatives and consistent estimation of jump times. In the process, we show that inference on the Hurst exponent of a rough fractional process is robust with respect to jumps. This provides an important insight for the growing literature on rough volatility. We demonstrate sound finite-sample properties in a simulation study and showcase the applicability of our methods in an empirical example with a time series of volatilities.

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arXiv2023

Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an It\^o semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic properties. The asymptotic analysis builds upon an expansion of tail probabilities for the order statistics based on a generalized arcsine law. In order to use the involved distribution of local order statistics for a bias correction, an efficient numerical algorithm is developed. We demonstrate the finite-sample performance of the estimation in a Monte Carlo simulation.

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arXiv2022

Efficient parameter estimation for parabolic SPDEs based on a log-linear model for realized volatilities

We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptotic regime. The asymptotic variances are shown to be substantially smaller compared to existing estimation methods. Moreover, asymptotic confidence intervals are directly feasible. Our approach builds upon realized volatilities and their asymptotic illustration as response of a log-linear model with spatial explanatory variable. This yields efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. We demonstrate efficiency gains compared to previous estimation methods numerically and in Monte Carlo simulations.

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arXiv2021

Gumbel convergence of the maximum of convoluted half-normally distributed random variables

In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution. Motivated by tests for jumps in high-frequency data, our main interest is in the half-normal distribution and the sum or difference of two independent half-normally distributed random variables. Since the half-normal distribution is neither stable nor symmetric, these examples are non-obvious generalizations. It is shown that the sum and difference of two independent half-normally distributed random variables and other examples yield distributions with tail behaviours that relate to the normal case. It turns out that the Gumbel convergence for all such distributions can be proved following similar steps. We illustrate the results in Monte Carlo simulations.

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arXiv2019

Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion

In this letter, we construct cusum change-point tests for the Hurst exponent and the volatility of a discretely observed fractional Brownian motion. As a statistical application of the functional Breuer-Major theorems by B\'egyn (2007) and Nourdin and Nualart (2019), we show under infill asymptotics consistency of the tests and weak convergence to the Kolmogorov-Smirnov law under the no-change hypothesis. The test is feasible and pivotal in the sense that it is based on a statistic and critical values which do not require knowledge of any parameter values. Consistent estimation of the break date under the alternative hypothesis is established. We demonstrate the finite-sample properties in simulations and a data example.

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arXiv2017

Change-point inference on volatility in noisy It\^o semimartingales

This work is concerned with tests on structural breaks in the spot volatility process of a general It\^o semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up on infill asymptotic results for certain functionals of spectral spot volatility estimates. A weak limit theorem is established under the null hypothesis relying on extreme value theory. We prove consistency of the test and of an associated estimator for the change point. A simulation study illustrates the finite-sample performance of the method and efficiency gains compared to a skip-sampling approach.

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arXiv2017

Volatility estimation for stochastic PDEs using high-frequency observations

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on squared increments. The estimator is consistent and admits a central limit theorem. This is established moreover for the joint estimation of the integrated volatility and parameters in the differential operator in a semi-parametric framework. Starting from a representation of the solution of the SPDE with Dirichlet boundary conditions as an infinite factor model and exploiting mixing-type properties of time series, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.

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arXiv2017

Estimating the Spot Covariation of Asset Prices - Statistical Theory and Empirical Evidence

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.

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arXiv2017

Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book

An extensive empirical literature documents a generally negative correlation, named the "leverage effect," between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect --- i.e. a relation between contemporaneous jumps in prices and volatility. The methods are robust to market microstructure noise and build on a newly developed price-jump localization and estimation procedure. Our empirical investigation of six years of transaction data from 320 NASDAQ firms displays no unconditional negative correlation between price and volatility cojumps. We show, however, that there is a strong relation between price-volatility cojumps if one conditions on the sign of price jumps and whether the price jumps are market-wide or idiosyncratic. Firms' volatility levels strongly explain the cross-section of discontinuous leverage while debt-to-equity ratios have no significant explanatory power.

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arXiv2015

Nonparametric change-point analysis of volatility

This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths comprising volatility jumps. This is embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency framework we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameter of fractional volatility processes. A simulation study demonstrates the practical value in finite-sample applications.

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arXiv2014

Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing

We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that the classes of multi-scale and kernel estimators for smoothing noise perturbation are asymptotically equivalent in the sense of having the same asymptotic distribution for corresponding kernel and weight functions. The theory leads to multi-dimensional stable central limit theorems and feasible versions. Hence they allow to draw statistical inference for a broad class of multivariate models which paves the way to tests and confidence intervals in risk measurement for arbitrary portfolios composed of high-frequently observed assets. As an application, we enhance the approach to construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.

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arXiv2014

Volatility estimation under one-sided errors with applications to limit order books

For a semi-martingale $X_t$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X, X \rangle_t$ is constructed based on observations in the vicinity of $X_t$. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive $n^{-1/3}$ as optimal convergence rate in a high-frequency framework with $n$ observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process $X_t$ from intra-day order book quotes.

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arXiv2014

Common price and volatility jumps in noisy high-frequency data

We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency data and is robust to market microstructure frictions. For the test, local estimators of volatility jumps at price jump arrival times are designed using a nonparametric spectral estimator of the spot volatility process. A simulation study and an empirical example with NASDAQ order book data demonstrate the practicability of the proposed methods and highlight the important role played by price volatility co-jumps.

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