Effect Of Microstructure Noise Research Articles

Retracted] Analysis of Factors Influencing Stock Market Volatility Based on GARCH‐MIDAS Model

This paper further extends the existing GARCH‐MIDAS model to deal with the effect of microstructure noise in mixed frequency data. This paper has two highlights. First, according to the estimation of the long‐term volatility components of the GARCH‐MIDAS model, rAVGRV is adopted to substitute for the RV estimator. rAVGRV uses the rich data sources in tick‐by‐tick data and significantly corrects the impact of the microstructure noise on volatility estimation. Second, besides introducing macroeconomic variables (i.e., macroeconomic consistency index (MCI), deposits in financial institutions (DFI), industrial value‐added (IVA), and M2), Chinese Economic Policy Uncertainty (CEPU) index and Infectious Disease Equity Market Volatility Tracker (EMV) are introduced in the long‐run volatility component of the GARCH‐MIDAS model. As indicated by the results of this paper, the rAVGRV‐based GARCH‐MIDAS is slightly better than the RV model‐based GARCH‐MIDAS. In addition to the common macroeconomic variables significantly impacting stock market volatility, CEPU also substantially impacts stock market volatility. Nevertheless, the effect of EMV on the stock market is insignificant.

Stochastic leverage effect in high-frequency data: a Fourier based analysis

The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The consistency of the estimator is proven. Moreover, its finite sample properties are studied in the presence of microstructure noise effects. The Fourier methodology is applied to S&P500 futures prices to investigate the magnitude of the stochastic leverage effect detectable at high-frequency.

Evaluating the Underlying Components of High Frequency Financial Data: Finite Sample Performance and Microstructure Noise Effects

This paper examines the finite sample properties of novel theoretical tests that evaluate the presence of: a) Brownian motion, b) jumps; c) finite vs. infinite activity jumps. In allowing for Gaussian, t-distributed, and Gaussian-T mixture noise, our Monte Carlo experiment guides a search for optimal performance across sampling frequencies. Using 100 stocks and SPY, we find that: i) a Brownian and a jump component characterize 1-min stock data; ii) Jumps should allow for both finite and infinite activity; iii) Rejection rates are time-varying, such that more jump days are usually associated with an increase of infinite jumps vis-a-vis finite jumps.

Rate efficient estimation of realized Laplace transform of volatility with microstructure noise

AbstractIn this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0,T] using high‐frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We use the pre‐averaging approach to deal with the effect of microstructure noise. Under the high‐frequency scenario, we obtain a consistent estimator whose convergence rate is , which is known as the optimal convergence rate of the estimation of integrated volatility functionals under the presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite‐sample performance of the proposed estimator.

On the inference about the spectral distribution of high-dimensional covariance matrix based on high-frequency noisy observations

In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is a signal-plus-noise sample covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of signal sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to consistently estimate the spectral distribution of ICV for a class of diffusion processes. An alternative approach is further proposed, which possesses several desirable properties: it is more robust, it eliminates the effects of microstructure noise, and the asymptotic relationship that enables consistent estimation of the spectral distribution of ICV is the standard Marčenko–Pastur equation. The performance of the two approaches is examined via simulation studies under both synchronous and asynchronous observation settings.

Realized Laplace Transform of Volatility with Microstructure Noise

In this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0, T] using high frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We employ the pre-averaging approach to deal with the effect of microstructure noise. Under the high frequency scenario, we obtain a consistent estimator whose convergence rate is ∆−1/4 n , which is known as the optimal convergence rate of the estimation of integrated volatility functionals under presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite sample performance of the proposed estimator.

Measuring the Intraday Jump Tail Risk of Financial Asset Price with Noisy High Frequency Data

This paper proposes a simple two-step nonparametric procedure to estimate the intraday jump tail and measure the jump tail risk in asset price with noisy high frequency data. We first propose the pre-averaging threshold approach to estimate the intraday jumps occurred, and then use the peaks-over-threshold (POT) method and generalized Pareto distribution (GPD) to model the intraday jump tail and further measure the jump tail risk. Finally, an empirical example further demonstrates the power of the proposed method to measure the jump tail risk under the effect of microstructure noise.

Spot volatility estimation using the Laplace transform

A new non-parametric estimator of the instantaneous volatility is defined relying on the link between the Laplace transform of the price process and that of the volatility process for Brownian semimartingale models. The proposed estimation method is a global one, in the spirit of methods based on Fourier series decomposition, with a plus for improving the precision of the volatility estimates near the boundary of the time interval. Consistency and asymptotic normality of the proposed estimator are proved. A simulation study confirms the theoretical results and Monte Carlo evidence of the favorable performance of the proposed estimator in the presence of microstructure noise effects is presented.

A simple microstructure return model explaining microstructure noise and Epps effects

We present a novel simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of both microstructure and macrostructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time-scale used to estimate it. The Epps effect states that cross correlations between asset returns are increasing functions of the time-scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time-scale in the presence of the long memory process (i).

A Simple Microstructure Return Model Explaining Microstructure Noise and Epps Effects

We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of intertrade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time scale used to estimate it. Paradoxically, the Epps effect states that cross correlations between asset returns are increasing functions of the time scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time scale in the presence of the long memory process (i).

Modelling and forecasting noisy realized volatility

Several methods have recently been proposed in the ultra-high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. As such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step-ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; (iii) even the partially corrected R 2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R 2 . An empirical example for S&P 500 data is used to demonstrate the techniques developed in this paper.

Jump-robust estimation of realized volatility in the EU Emission Trading Scheme

With the increased availability of high-frequency financial market data in recent years, the extraction of "realized" volatility (from intraday squared returns) has led to numerous theoretical developments and empirical applications for a wide range of equity and commodity markets. This paper documents the measure of realized volatility in the European Union Emission Trading Scheme (EU ETS) with respect to the presence of microstructure noise and jumps in the estimation procedure. In order to include jumps in the modeling of CO2 intraday volatility returns, we use the bipower variation measure as well as the more recent median realized volatility estimator. To deal with microstructure noise effects we apply Awartani et al's ZT test to the price series of CO2 intraday futures for both bipower variation and median realized volatility and identify 20-minute returns as the optimal sampling frequency. Subsequently, the empirical analysis of both bipower variation and median realized volatility measures for CO2 prices reveals the presence of around 5% of "significant" jumps, especially during the "panicto-cash" period of October 2008 in the EU ETS, and a lower range of estimates (around [0;0:15] for bipower variation and [0;0:10] for median realized volatility) compared with the "naive" estimator (around [0;0:23]).

Estimating covariation: Epps effect, microstructure noise

This paper is about how to estimate the integrated covariance 〈 X , Y 〉 T of two assets over a fixed time horizon [ 0 , T ] , when the observations of X and Y are “contaminated” and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. This is an analytic characterization of the Epps effect. We also provide the optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization. Finally, a two scales covariance estimator is provided which simultaneously cancels (to first order) the Epps effect and the effect of microstructure noise. The gain is demonstrated in data.

On the Microstructural Hedging Error

We consider the issue of hedging a European derivative security in the presence of microstructure noise. In a market where the efficient price of the asset is driven by a stochastic volatility process, we assume an agent wants to use a (possibly misspecified) local volatility-type replication strategy. Focusing on microstructure noise effects, our goal is to evaluate the error between the theoretical, but practically unfeasible, strategy and its market adapted versions. The microstructural hedging error is in particular due to transaction price discreteness and endogenous trading times. Thus, we consider a transaction price model that accommodates such inherent properties of ultrahigh frequency data with the assumption of a continuous semimartingale efficient price. In this framework, we study two hedging strategies derived from the local volatility-type hedging strategy: (i) the hedging portfolio is rebalanced every time that the transaction price moves; (ii) the hedging portfolio is rebalanced only once the transaction price has varied by more than a selected value. To assess these strategies, we use an asymptotic approach where the number of rebalancing transactions goes to infinity. For the first strategy, we show that, because of microstructure noise effects, the hedging error does not vanish. However, an optimal strategy of the second type enables us to reduce it significantly.

Assessing Market Microstructure Effects via Realized Volatility Measures with an Application to the Dow Jones Industrial Average Stocks

Transaction prices of financial assets are contaminated by market microstructure effects. This is particularly relevant when estimating volatility using high frequency data. In this article, we assess statistically the effect of microstructure noise on volatility estimators, and test the hypothesis that its variance is independent of the sampling frequency. We provide evidence based on the Dow Jones Industrial Average stocks. We find that noise has a statistically significant effect on volatility estimators at frequencies of 2–3 min or higher. The independently and identically distributed specification with constant variance seems to be a plausible model for microstructure noise, except for ultra high frequencies.

Modelling and Forecasting Noisy Realized Volatility

Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent (modified) realized volatility (RV) estimates of the integrated volatility can contain residual microstructure noise and other measurement errors. Such noise is called “realized volatility error”. As such measurement errors ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators due to model misspecification; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of , which can be applied to linear and nonlinear, short and long memory models. An empirical example for S&P 500 data is used to demonstrate that neglecting RV errors can lead to serious bias in estimating the model of integrated volatility, and that the new method proposed here can eliminate the effects of the RV noise. The empirical results also show that the full correction for is necessary for an accurate description of goodness-of-fit.

Forecasting performance of extreme‐value volatility estimators

AbstractThis study evaluates the forecasting performance of extreme‐value volatility estimators for the equity‐based Nifty Index using two‐scale realized volatility. This benchmark mitigates the effect of microstructure noise in the realized volatility. Extreme‐value estimates with relatively simple forecasting methods provide substantially better short‐term and long‐term forecasts, compared to historical volatility. The higher efficiency of extreme‐value estimators is primarily responsible for this improvement. The extent of possible improvement in forecasts is likely to be economically significant for applications like options pricing. By including extremevalue estimators, the forecasting performance of generalized autoregressive conditional heteroscedasticity (GARCH) can also be improved. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27: 1085–1105, 2007