Presence Of Market Microstructure Noise Research Articles

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

A 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.

Nothing but noise? Price discovery across cryptocurrency exchanges

We examine the price discovery contributions of cryptocurrency exchanges in the presence of market microstructure noise. Cryptocurrency markets exhibit a decisively higher level of microstructure noise compared with the NYSE or NASDAQ. Therefore, traditional measures of price discovery could be biased. To overcome this concern, we draw on the information leadership share proposed by Putniņš (2013); by leveraging this information, we find that Bitfinex is the leader in the price discovery process. These results highlight the importance of accounting for different levels of noise when evaluating price discovery contributions.

Nothing but Noise? Price Discovery between Cryptocurrency Exchanges

We examine the price discovery contributions of cryptocurrency exchanges in the presence of market microstructure noise. Cryptocurrency markets exhibit a decisively higher level of microstructure noise compared to the New York Stock Exchange or NASDAQ. Therefore, traditional measures of price discovery are potentially biased. To overcome this concern, we draw on the information leadership share (ILS) proposed by Putnins [2013, J.Emp.Fin]. Based on the ILS, we find that Bitfinex is the leader in the price discovery process. Our results highlight the importance of accounting for different levels of noise when evaluating price discovery contributions

Оценщики квадратичной вариации основанные на высокочастотных данных – эмпирический обзор

Recently, advances in computer technology and data recording and storage have made high-frequency financial data readily available to researchers. As a result, the volatility literature has steadily progressed toward the use of higher-frequency data. However, the move towards the use of higher-frequency financial data in the estimation of volatility of financial returns has resulted in the development of many realised volatility measures of asset return variability based on a variety of different assumptions and functional forms and thus making theoretical comparison and selection of the estimators for empirical applications very difficult if not impossible. This article provides an empirical review on the performance of estimators of quadratic variation/integrated variance based on high-frequency data to aid their application in empirical analysis. The result of the review shows that no single estimator works best in all situations; however, the more sophisticated realised measures, in particular the TSRV and KRV, are superior to the other estimators in terms of their estimation accuracy in the presence of market microstructure noise.

Detecting price jumps in the presence of market microstructure noise

ABSTRACT In this paper we design a test to detect the arrivals of jumps in asset prices contaminated by market microstructure noise. This test is defined by means of the truncated two-scales realised volatility estimator, recently introduced in Brownlees, Nualart, and Sun [2019, ‘On the Estimation of Integrated Volatility in the Presence of Jumps and Microstructure Noise’, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2791342.], which is a robust estimator of the realised volatility in the presence of price jumps and market microstructure noise. We derive the asymptotic value of the power of the test given the significance level, and provide conditions for the test to be consistent. Simulations show that the test performs satisfactorily when the sampling frequency is high. In particular, we show that the test performs better than some prevalent jump tests. We also provide a real data example to illustrate the proposed method.

A Hausman test for the presence of market microstructure noise in high frequency data

We develop tests that help assess whether a high frequency data sample can be treated as reasonably free of market microstructure noise at a given sampling frequency for the purpose of implementing high frequency volatility and other estimators. The tests are based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. We investigate the asymptotic properties of the test statistic in a general nonparametric setting, and compare it with several alternatives that are also developed in the paper. Empirically, we find that improvements in stock market liquidity over the past decade have increased the frequency at which simple, uncorrected, volatility estimators can be safely employed.

Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of maximum-likelihood- and Bayes-type estimators based on it. We also prove the local asymptotic normality of the model and asymptotic efficiency of our estimator when the diffusion coefficients are deterministic and noise follows a normal distribution. We conjecture that our estimator is asymptotically efficient even when the latent process is a general diffusion process. An estimator for the quadratic covariation of the latent process is also constructed. Some numerical examples show that this estimator performs better compared to existing estimators of the quadratic covariation.

A Hausman Test for the Presence of Market Microstructure Noise in High Frequency Data

We develop tests that help assess whether a high frequency data sample can be treated as reasonably free of market microstructure noise at a given sampling frequency for the purpose of implementing high frequency volatility and other estimators. The tests are based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. We investigate the asymptotic properties of the test statistic in a general nonparametric setting, and compare it with several alternatives that are also developed in the paper. Empirically, we find that improvements in stock market liquidity over the past decade have increased the frequency at which simple, uncorrected, volatility estimators can be safely employed.

Increased correlation among asset classes: Are volatility or jumps to blame, or both?

We develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components, in a manner that is robust to the presence of market microstructure noise. Using high frequency data on different assets classes, we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations. However, we find little evidence to suggest a change between the relative contributions of the Brownian and jump components, as both comove. Co-jumps stem from surprising news announcements that occur primarily before the opening of the US market, and are also accompanied by an increase in Brownian-driven correlations.

Realised Co-Skewness of the VIX and S&P 500 and the Equity Premium

We provide theoretical and empirical justifications for linking the realised co-skewness between the VIX and the S&P 500 to conditional equity premiums. The realised co-skewness, as a measure of hedging benefits, shows a significant (and independent to that of the variance risk premium) negative prediction for the next month equity premium. We also present a new measure of higher co-moments using high frequency data under the general jump diffusion model. The estimator is robust to the presence of market microstructure noise and can be extended to other co-moment measurement in current risk management practices.

Testing for jumps in noisy high frequency data

This paper proposes a robustification of the test statistic of Aït-Sahalia and Jacod (2009b) for the presence of market microstructure noise in high frequency data, based on the pre-averaging method of Jacod et al. (2010). We show that the robustified statistic restores the test’s discriminating power between jumps and no jumps despite the presence of market microstructure noise in the data.

Best Quadratic Unbiased Estimators of Integrated Variance in the Presence of Market Microstructure Noise

We consider the best quadratic unbiased estimators of the integrated variance in the presence of independent market microstructure noise. We establish the asymptotic normality of a feasible best quadratic unbiased estimator under the assumption of constant

Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data

Abstract. We focus on estimating the integrated covariance of log‐price processes in the presence of market microstructure noise. We construct a consistent asymptotically unbiased estimator for the quadratic covariation of two Itô processes in the case where high‐frequency asynchronous discrete returns under market microstructure noise are observed. This estimator is based on synchronization and multi‐scale methods and attains the optimal rate of convergence. A lower bound for the rate of convergence is derived from the local asymptotic normality property of the simpler parametric model with equidistant and synchronous observations. A Monte Carlo study analyses the finite sample size characteristics of our estimator.

Frequency Domain Estimation of Integrated Volatility for Itô Processes in the Presence of Market-Microstructure Noise

This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency by frequency, and the concept of the multiscale ratio is introduced to quantify the bias in the realized integrated volatility due to the observation error. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed, which simultaneously reduces variance. We extend the method to include correlated observation errors and provide the implied time-domain form of the estimation procedure. The new method is implemented to estimate the integrated volatility for the Heston and other models, and the improved performance of our method over existing methods is illustrated by simulation studies.

Bias-Correcting the Realized Range-Based Variance in the Presence of Market Microstructure Noise

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has lead to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5- or 15-minute returns. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to the range-statistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise. We can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it using Microsoft high-frequency data from TAQ. We find that a bias-corrected range-statistic often leads to much smaller confidence intervals for the integrated variance, relative to the realized variance.

Bias-correcting the realized range-based variance in the presence of market microstructure noise

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has led to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5- or 15-minute returns. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias correction to the range-statistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise. We can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it using Microsoft high-frequency data from TAQ. We find that a bias-corrected range-statistic often leads to much smaller confidence intervals for the integrated variance, relative to the realized variance.

Dynamic Portfolio Management: An Application of Fourier Method for Covariance Estimation

The economic benefit of applying the Fourier covariance estimation methodology over other estimators in the presence of market microstructure noise is studied from the perspective of an asset-allocation decision problem. We find that using Fourier methodology yields statistically significant gains.

Out of sample forecasts of quadratic variation

We compare the forecasts of Quadratic Variation given by the Realized Volatility (RV) and the Two Scales Realized Volatility (TSRV) computed from high frequency data in the presence of market microstructure noise, under several different dynamics for the volatility process and assumptions on the noise. We show that TSRV largely outperforms RV, whether looking at bias, variance, RMSE or out-of-sample forecasting ability. An empirical application to all DJIA stocks confirms the simulation results.

Microstructure Noise, Realized Variance, and Optimal Sampling

A recent and extensive literature has pioneered the summing of squared observed intra-daily returns, variance, to estimate the daily integrated variance of financial asset prices, a traditional object of economic interest. We show that, in the presence of market microstructure noise, realized variance does not identify the daily integrated variance of the frictionless equilibrium price. However, we demonstrate that the noise-induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high-frequency sampling and derive a mean-squared-error (MSE) optimal sampling theory for the purpose of integrated variance estimation. We show how our theory naturally leads to an identification procedure, which allows us to recover the moments of the unobserved noise; this procedure may be useful in other applications. Finally, using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric, we find that explicit optimization of realized variance's finite sample MSE properties results in accurate forecasts and considerable economic gains. Copyright 2008, Wiley-Blackwell.

Using High-Frequency Data in Dynamic Portfolio Choice

This article evaluates the economic benefit of methods that have been suggested to optimally sample (in an MSE sense) high-frequency return data for the purpose of realized variance/covariance estimation in the presence of market microstructure noise (Bandi and Russell, 2005a, 2008). We compare certainty equivalents derived from volatility-timing trading strategies relying on optimally-sampled realized variances and covariances, on realized variances and covariances obtained by sampling every 5 minutes, and on realized variances and covariances obtained by sampling every 15 minutes. In our sample, we show that a risk-averse investor who is given the option of choosing variance/covariance forecasts derived from MSE-based optimal sampling methods versus forecasts obtained from 5- and 15-minute intervals (as generally proposed in the literature) would be willing to pay up to about 80 basis points per year to achieve the level of utility that is guaranteed by optimal sampling. We find that the gains yielded by optimal sampling are economically large, statistically significant, and robust to realistic transaction costs.