Microstructure Noise Research Articles

Market Microstructure Noise, Intraday Stock Market Returns, and Adaptive Learning: Indian Evidence

What drives intraday traders’ sentiments in the stock markets: information or noise? This paper argues that the market microstructure noise (MMN) manifests intraday traders’ aggregate sentiments depicted by chaotic and noisy market returns. It examines if intraday stock market returns, returns’ variances and higher order moments are erratic, noisy and non-normal. It shows that the intraday Bombay Stock Exchange (BSE) Sensex and National Stock Exchange (NSE) Nifty index returns approximate to zero-mean, zero-variance but skewed and leptokurtic in distributions. In exploring the intraday market index returns, standardisation process reveals noises in the BSE market, but it is evened up in the NSE market. Since intraday traders’ market sentiments and decision choices are behavioural, noisy but adaptive, their decision choices need strategies given that those strategies have numerical “attractions” that determine choice probabilities. We explore the adaptive Experience Weighted Attraction (EWA) learning parameters to show persistent MMN in intraday traders’ adaptive learning behaviours.

Challenges of integrated variance estimation in emerging stock markets

Estimating integrated variance, using high frequency data, requires modelling experience and data crunching skills. Although intraday returns have attracted much attention in recent years, handling these data is challenging because of their unique characteristics. When dealing with ultra-high frequency or tick-by-tick observations the enormous amount of data needs to be processed prior to estimation of integrated variance for two reasons: eliminating microstructure noise and finding appropriate unbiased estimator. This paper contributes to the existing literature in a two ways. First, we propose how to handle quality issues of the high frequency data due to non-frequent trading and lower liquidity of emerging markets. Second, we find the optimal sampling frequency at slow time scale that should be used to obtain two-time scale estimator of integrated variance for each emerging market under consideration: Romania, Hungary, Bulgaria and Croatia. Empirical results indicate that intraday returns should be sampled every 7 to 10 minutes at slow time scale while the fast time scale should be fixed at the highest possible frequency. Realized variance estimator at the fast time scale mostly overestimates the integrated variance on all stock markets except Bulgaria; on average between 70% and 90% of the time. Moreover, the robustness of the results with respect to the price jumps has been verified for Romania and Hungary, unlike Croatia and Bulgaria, for which we recommend a robust version of two-time scale estimator of integrated variance within truncation technique. It is additionally found that intraday returns should be sampled more frequently in a highly volatile periods. These findings offer valuable information to market participants, as they are able to apply the most accurate ex-post volatility measure, as unbiased and consistent estimate of integrated variance.

High frequency traders and the price process

Using a dataset that uniquely identifies counterparties to each S&P500 eMini transaction, we classify each market participant as high or low frequency, and each transaction, by the speed of the traders involved. We investigate empirically the comparative influence of high and low frequency traders on the price process, and conversely the influence of the price process on the trading of high and low frequency traders. We find that high frequency traders have a particularly high success rate on each transaction, measured by the likelihood that the following price change will go in their direction as well as by the amount of time they have to wait to realize their gain, when trading against low frequency traders. Contrary to common wisdom, we find that high frequency traders’ activity does not induce volatility or jumps. In fact, it is their absence that is problematic: volatility and jumps are more prevalent in periods when they trade less intensely. Conversely, we find that spikes in volatility and jumps cause high frequency traders to trade less intensely, decreasing their provision of liquidity. Finally, looking at the market microstructure noise component to the price model, we find that higher level of noise generates trading opportunities for high frequency traders and lead them to increase their trading activity.

A Generalized Heterogeneous Autoregressive Model using the Market Index

This paper shows that generalizing the heterogeneous autoregressive model (HAR) with realized (co)variances and semi-(co)variances from the index leads to more accurate volatility forecasts. To circumvent the effects of the market microstructure noise arising from using high sampling frequencies, we adopt noise-robust estimators for the realized (co)variances and develop novel noise-robust estimators for the semi-(co)variances. To explore the sampling frequency at which the forecasting gains are maximized, we adopt a mixed-sampling approach that iterates over several sampling frequencies of the stock and the index. Our analysis shows that gains are maximized at the combination of a low (high) frequency on the stock (index). We illustrate that the observed forecasting gains translates into economic gains such that a risk-averse investor is willing to pay up to 57 annual basis points by adopting a model specification that utilizes the index information.

Bayesian Nonparametric Estimation ofEx PostVariance

AbstractVariance 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.

Dependent microstructure noise and integrated volatility estimation from high-frequency data

In this paper, we develop econometric tools to analyze the integrated volatility (IV) of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive consistent estimators of the IV, which converge stably to a mixed Gaussian distribution at the optimal rate n1∕4. To improve the finite sample performance, we propose a multi-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our multi-step estimators. In an empirical study, we analyze the dependence structures of microstructure noise and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating IV.

High-dimensional minimum variance portfolio estimation based on high-frequency data

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which provide reference targets. Simulation and empirical studies demonstrate the favorable performance of the proposed portfolios.

Jumps at Ultra-High Frequency: Evidence From the Chinese Stock Market

This paper proposes a new jump test for semi-martingale contained by microstructure noise based on the threshold pre-averaging bi-power estimation. Theoretically, we prove that such test has asymptotical size and power. Monte Carlo simulations show that the new test has better performance than Christensen et al(2014)'s test in noisy setting and we also consider adopting the false discovery rate (FDR) threshold technique to avoid spurious detections. In the empirical part, we investigate the contributions of jumps to total return variance from the Chinese stock market based on the tick-by-tick transaction data. The empirical results imply that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature from different perspectives.

Conditionally Gaussian random sequences for an integrated variance estimator with correlation between noise and returns

AbstractCorrelation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the financial literature are not designed to explicitly handle such a dependence, or handle it only in special settings. We provide an integrated variance estimator that is robust to correlated noise and returns. For this purpose, a generalization of the forward filtering backward sampling algorithm is proposed, to provide a sampling technique for a latent conditionally Gaussian random sequence. We apply our methodology to intraday Microsoft prices and compare it in a simulation study with established alternatives, showing an advantage in terms of root‐mean‐square error and dispersion.

Robust estimation of risk‐neutral moments

AbstractThis study provides an in‐depth analysis of how to estimate risk‐neutral moments robustly. A simulation and an empirical study show that estimating risk‐neutral moments presents a trade‐off between (a) the bias of estimates caused by a limited strike price domain and (b) the variance of estimates induced by microstructural noise. The best trade‐off is offered by option‐implied quantile moments estimated from a volatility surface interpolated with a local‐linear kernel regression and extrapolated linearly. A similarly good trade‐off is achieved by estimating regular central option‐implied moments from a volatility surface interpolated with a cubic smoothing spline and flat extrapolation.

A ReMeDI for Microstructure Noise

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high-frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes and data frequencies.

A Machine Learning Approach to Estimating Large Positive Definite Covariance Matrix of High Frequency Data

This paper proposes a novel covariance estimator via a machine learning approach when both the sampling frequency and covariance dimension are large. Assuming that a large covariance matrix can be decomposed into low rank and sparse components, our method simultaneously provides a consistent estimation of these two components in a one-step procedure. Moreover, in the presence of microstructure noises and asynchronous trading, the covariance estimator is guaranteed to be positive definite with the optimal rate of convergence. Taking into account the serial dependent feature of financial data, we further provide a data-driven algorithm to select the optimal tuning parameters in practice. We apply the proposed estimator to vast portfolio allocations, which enjoy significantly enhanced out-of-sample portfolio risk and Sharpe ratios. The success of our approach helps justify the role that machine learning techniques play in finance.

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.

What Makes Cryptocurrencies Special? Investor Sentiment and Return Predictability During the Bubble

We propose a crypto-specific lexicon to quantify the investor sentiment and use it to predict the cryptocurrency market returns. The new lexicon achieves better accuracy (32\% higher) than the traditional financial lexicon when applied to an out-of-sample classification setting. The empirical results reveal that investor sentiment positively predicts excess CRIX returns with a daily in(out)-of-sample $R^2$ of 2.74\% (3.15\%) without significant evidence on the return reversal. The results are robust to the inclusion of alternative sentiment indices, technical indicators, market microstructure noise, and across bubble and non-bubble periods. We further exclude the soft information interpretation of our sentiment index by showing that non-fundamental related sentiment shows stronger predictive power than that of the fundamentally related sentiment. Our findings suggest that in a market-driven by noise traders, and when there is only limited information about the fundamental value of the underlying asset, investor sentiment drives the price evolution and its impact may not reverse in a short horizon.

Disentangling Sources of High Frequency Market Microstructure Noise

Employing tick-by-tick maximum likelihood estimation on several leading models from the financial economics literature, we find that the market microstructure noise is mostly explained by a linear model where the trade direction, that is, whether the trade is buyer or seller initiated, is multiplied by the dynamic quoted bid-ask spread. Although reasonably stable intraday, this model manifests variability across days and stocks. Among different observable high frequency financial characteristics of the underlying stocks, this variability is best explained by the tick-to-spread ratio, implying that discreteness is the first residual source of noise. We determine the bid-ask bounce effect as the next source of noise.

High-Dimensional Minimum Variance Portfolio Estimation Based on High-Frequency Data

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which provide reference targets. Simulation and empirical studies demonstrate the favorable performance of the proposed portfolios.

Estimation of volatility in a high-frequency setting: a short review

Our aim is to give an overview of the topic of estimation of volatility, in a high-frequency setting. We emphasize the various possible situations, relative to the underlying process (continuous, or with jumps having finite, or infinite, activity) and to the observation scheme (with microstructure noise or not, under a regular sampling scheme or not). We try to explain a variety of methods, including the most recent ones. Each method is quickly sketched, with comments on its range of applicability. Most results are given in the form of a theorem, with a precise description of the assumptions needed, but of course without proof, and some results are simply mentioned in a somewhat loose way. We consider only the one-dimensional case, although occasional comments are made about the multivariate case. We totally omit the nowadays hot topic when the number of assets is very large, meaning that this number increases as the frequency increases: this is unfortunately not compatible with a “short” review as this one.

Make-take decisions under high-frequency trading competition

The make-take preferences of investors depend on high-frequency trading (HFT) competition, under which HFT firms endogenously acquire speed and informational advantages. In the case where there are many HFT firms in the market, they compete more through limit orders; meanwhile, in the case with few HFT firms, they compete more through market orders that “pick-off" limit orders coming from the big crowd of slow traders. In the former (latter) case, additional HFT competition improves (damage) liquidity. In both cases, HFT competition improves informational efficiency and reduces microstructure noise. Finally, I use the model to analyze potential regulations under HFT competition.

The signal and the noise volatilities

This paper explores the volatility forecasting implications of a model in which the high-frequency market microstructure noise is related to the true underlying volatility. The contribution of this paper is to propose a theoretical framework under which the realized variance, based on the highest frequency to compute returns, may improve volatility forecasting if the noise variance is an affine function of the fundamental volatility. In this new setting, we extend the work of Andersen et al. (2011) and quantify the predictive ability of several measures of integrated variance. We find that the traditional realized variance based on the highest frequency returns outperforms alternative realized measures. We also evaluate the usefulness of our approach by conducting an empirical application and show several improvements resulting from the assumption of time-varying noise variance.

High-dimensional multivariate realized volatility estimation

We provide a new factor-based estimator of the realized covolatility matrix, applicable in situations when the number of assets is large and the high-frequency data are contaminated with microstructure noises. Our estimator relies on the assumption of a factor structure for the noise component, separate from the latent systematic risk factors that characterize the cross-sectional variation in the frictionless returns. The new estimator provides theoretically more efficient and finite-sample more accurate estimates of large-scale integrated covolatility and correlation matrices than other recently developed realized estimation procedures. These theoretical and simulation-based findings are further corroborated by an empirical application related to portfolio allocation and risk minimization involving several hundred individual stocks.