scholarly journals ESTIMATION OF INTEGRATED COVARIANCES IN THE SIMULTANEOUS PRESENCE OF NONSYNCHRONICITY, MICROSTRUCTURE NOISE AND JUMPS

2015 ◽  
Vol 32 (3) ◽  
pp. 533-611 ◽  
Author(s):  
Yuta Koike
Keyword(s):  
High Frequency ◽  
Monte Carlo Study ◽  
Jump Processes ◽  
Observation Data ◽  
Observation Error ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Sampling Schemes ◽  
Integrated Covariance ◽  
Asymptotic Mixed Normality

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a high frequency. This new estimator, which we call the pre-averaged truncated Hayashi–Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data are polluted by some noise. We also show the asymptotic mixed normality of this estimator under some mild conditions allowing infinite activity jump processes with finite variations, some dependency between the sampling times and the observed processes as well as a kind of endogenous observation error. We examine the finite sample performance of this estimator using a Monte Carlo study and we apply our estimators to empirical data, highlighting the importance of accounting for jumps even in an ultra-high frequency framework.

High-Frequency Financial Econometrics

2014 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Jean Jacod
Keyword(s):  
High Frequency ◽  
Practical Importance ◽  
Financial Econometrics ◽  
Trading Strategies ◽  
Financial Data ◽  
Jump Processes ◽  
High Frequency Trading ◽  
Microstructure Noise ◽  
Econometric Methods ◽  
Mathematical Foundations

High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. The book covers the mathematical foundations of stochastic processes, describes the primary characteristics of high-frequency financial data, and presents the asymptotic concepts that their analysis relies on. It also deals with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As the book demonstrates, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. The book approaches high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

2020 ◽  
pp. 1-43
Author(s):  
Torben G. Andersen ◽  
Nicola Fusari ◽  
Viktor Todorov ◽  
Rasmus T. Varneskov
Keyword(s):  
Spatial Dependence ◽  
Option Price ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Testing Procedure ◽  
Observation Error ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Observation Times ◽  
Index Option

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA

2013 ◽  
Vol 29 (4) ◽  
pp. 838-856 ◽  
Author(s):  
Minjing Tao ◽  
Yazhen Wang ◽  
Xiaohong Chen
Keyword(s):  
Sample Size ◽  
High Frequency ◽  
Convergence Rates ◽  
Fast Convergence ◽  
High Frequency Data ◽  
Frequency Data ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Integrated Volatility ◽  
The Matrix

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the number of assets and the sample size go to infinity, we show that our new estimator is consistent and achieves a fast convergence rate, where the rate is optimal with respect to the sample size. A simulation study is conducted to check the finite sample performance of the proposed estimator.

Statistical Inference of Spot Correlation and Spot Market Beta under Infinite Variation Jumps*

2020 ◽  
Author(s):  
Qiang Liu ◽  
Zhi Liu
Keyword(s):  
Statistical Inference ◽  
High Frequency ◽  
Order Approximation ◽  
Estimation Procedure ◽  
Spot Market ◽  
Jump Processes ◽  
Empirical Characteristic Function ◽  
Finite Sample ◽  
Market Beta ◽  
The Individual

Abstract Empirical evidence has revealed that the jumps in financial markets appear to be very frequent. This study considers the statistical inference of the spot correlation and the spot market beta between two different assets using high-frequency data, in a setting where both the cojumps and the individual jumps in the underlying driving processes could be of infinite variation. Starting from the estimation of the spot covariance, we propose consistent estimators of the spot correlation and the spot market beta when the jump processes involved are general semimartingales. The second-order approximation for the estimators, namely, the central limit theorems, is established under the assumption that the jumps around zero are of stable Lévy type. Our estimation procedure is based on the empirical characteristic function of the increments of the processes and the application of the polarization identity; the bias terms stemming from the jumps are removed iteratively. The finite sample performances of the proposed estimators and other existing estimators are assessed and compared by using datasets simulated from various models. Our estimators are also applied to some real high-frequency financial datasets.

Pre-averaging estimate of high dimensional integrated covariance matrix with noisy and asynchronous high-frequency data

2018 ◽  
Vol 07 (03) ◽  
pp. 1850005 ◽  
Author(s):  
Zhi Liu ◽  
Xiaochao Xia ◽  
Guoliang Zhou
Keyword(s):  
Covariance Matrix ◽  
High Frequency ◽  
Rapid Development ◽  
Global Market ◽  
High Frequency Data ◽  
High Dimensional ◽  
Frequency Data ◽  
Microstructure Noise ◽  
Matrix Estimation ◽  
Integrated Covariance

With rapid development of the global market, the number of financial securities has significantly grown, which greatly challenges the measuring of financial quantities. Among others, the estimation of covariance matrix which plays an important role in risk management becomes no longer accurate. In this paper, we consider the estimation of integrated covariance matrix of semi-martingales under framework of high dimension by using high frequency data. We assume that the multivariate asset prices are observed asynchronously and all the observed prices are contaminated by microstructure noise. We employ the pre-averaging method to remove the microstructure noise and the generalized synchronization method to deal with the non-synchronicity. Moreover, to avoid the inconsistency in the high-dimensional covariance matrix estimation, we propose a regularized estimate. The consistency under matrix [Formula: see text]-norm is established. Compared to existing results, our estimator improves the accuracy of the estimation. Finally, we assess the theoretical results via some simulation studies.

scholarly journals Detecting factors of quadratic variation in the presence of market microstructure noise

2021 ◽  
Author(s):  
Naoto Kunitomo ◽  
Daisuke Kurisu
Keyword(s):  
Maximum Likelihood ◽  
Market Microstructure ◽  
High Frequency ◽  
Quadratic Variation ◽  
Financial Data ◽  
Likelihood Method ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Latent Factors ◽  
Market Microstructure Noise

AbstractA method of detecting latent factors of quadratic variation (QV) of Itô semimartingales from a set of discrete observations is developed when the market microstructure noise is present. We propose a new way to determine the number of latent factors of quadratic co-variations of asset prices based on the SIML (separating information maximum likelihood) method by Kunitomo et al. (Separating information maximum likelihood estimation for high frequency financial data. Springer, Berlin, 2018). In high-frequency financial data, it is important to investigate the effects of possible jumps and market microstructure noise existed in financial markets. We explore the estimated variance–covariance matrix of latent (efficient) prices of the underlying Itô semimartingales and investigate its characteristic roots and vectors of the estimated quadratic variation. We give some simulation results to see the finite sample properties of the proposed method and illustrate an empirical data analysis on the Tokyo stock market.

scholarly journals Bayesian Nonparametric Estimation of Ex Post Variance*

2019 ◽  
Author(s):  
Jim Griffin ◽  
Jia Liu ◽  
John M Maheu
Keyword(s):  
High Frequency ◽  
Variance Estimation ◽  
Bayesian Nonparametric ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Classical Counterpart ◽  
Variance Estimators ◽  
Ex Post ◽  
Bayesian Nonparametric Methods ◽  
Bayesian Nonparametric Estimation

Abstract Variance estimation is central to many questions in finance and economics. Until now ex post variance estimation has been based on infill asymptotic assumptions that exploit high-frequency data. This article offers a new exact finite sample approach to estimating ex post variance using Bayesian nonparametric methods. In contrast to the classical counterpart, the proposed method exploits pooling over high-frequency observations with similar variances. Bayesian nonparametric variance estimators under no noise, heteroskedastic and serially correlated microstructure noise are introduced and discussed. Monte Carlo simulation results show that the proposed approach can increase the accuracy of variance estimation. Applications to equity data and comparison with realized variance and realized kernel estimators are included.

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