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31
Realized Variance and Market Microstructure Noise
, 2005
"... We study market microstructure noise in highfrequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernelbased estimators can unearth important characteristics of market microstructure noise and that a simple kernelbas ..."
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Cited by 264 (14 self)
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We study market microstructure noise in highfrequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernelbased estimators can unearth important characteristics of market microstructure noise and that a simple kernelbased estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise is timedependent and correlated with increments in the efficient price. This has important implications for volatility estimation based on highfrequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid–ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient price.
Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility
 REVIEW OF ECONOMICS AND STATISTICS, FORTHCOMING
, 2006
"... A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNi ..."
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Cited by 164 (10 self)
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A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNielsen and Shephard (2004a, 2005) for related bipower variation measures, the present paper provides a practical and robust framework for nonparametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from nonjump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the nonjump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.
MICROSTRUCTURE NOISE, REALIZED VARIANCE, AND OPTIMAL SAMPLING
, 2005
"... Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sam ..."
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Cited by 98 (9 self)
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Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sample effects of general market microstructure noise on realized variance estimates. The finite sample results culminate in a variance/bias tradeoff that serves as a basis for an optimal sampling theory. Our theory also considers the effects of prefiltering the data and proposes a novel biascorrection. We show that this theory is easily implementable in practise requiring only the calculation of sample moments of the observable highfrequency return data.
Regular and Modified KernelBased Estimators of Integrated Variance: The Case with Independent Noise
, 2004
"... We consider kernelbased estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernelbased estimators and derive a lower bound for their asymptotic variance. Further we show that the subsamplebased ..."
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Cited by 51 (9 self)
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We consider kernelbased estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernelbased estimators and derive a lower bound for their asymptotic variance. Further we show that the subsamplebased estimator is closely related to a Bartletttype kernel estimator. The small difference between the two estimators due to end effects, turns out to be key for the consistency of the subsampling estimator. This observation leads us to a modified class of kernelbased estimators, which are also consistent. We study the efficiency of our new kernelbased procedure. We show that optimal modified kernelbased estimator converges to the integrated variance at rate m 1/4, where m is the number of intraday returns.
A DiscreteTime Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects
, 2007
"... We develop an empirically highly accurate discretetime daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from highfrequency intraday dat ..."
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Cited by 47 (5 self)
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We develop an empirically highly accurate discretetime daily stochastic volatility model that explicitly distinguishes between the jump and continuoustime components of price movements using nonparametric realized variation and Bipower variation measures constructed from highfrequency intraday data. The model setup allows us to directly assess the structural interdependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easytoimplement auxiliary model in the context of indirect estimation of empirically more realistic continuoustime jump diffusion and Lévydriven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the highfrequency intraday data.
Realized RangeBased Estimation of Integrated Variance
 JOURNAL OF FINANCIAL ECONOMETRICS (FORTHCOMING
, 2005
"... We provide a set of probabilistic laws for estimating quadratic variation of continuous semimartingales with the realized rangebased variance; a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available ..."
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Cited by 26 (2 self)
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We provide a set of probabilistic laws for estimating quadratic variation of continuous semimartingales with the realized rangebased variance; a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available and given weak conditions our statistic is consistent and has a mixed Gaussian limit with five times the precision of realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to give a consistent, mixed normal estimator, irrespective of nontrading. It has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the highlow. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest the empirical path of quadratic variation is also estimated better with the intraday highlow statistic.
An Unbiased Measure of Realized Variance
, 2004
"... The realized variance (RV) is known to be biased because intraday returns are contaminated with market microstructure noise, in particular if intraday returns are sampled at high frequencies. In this paper, we characterize the bias under a general specification for the market microstructure noise, ..."
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Cited by 13 (1 self)
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The realized variance (RV) is known to be biased because intraday returns are contaminated with market microstructure noise, in particular if intraday returns are sampled at high frequencies. In this paper, we characterize the bias under a general specification for the market microstructure noise, where the noise may be autocorrelated and need not be independent of the latent price process. Within this framework, we propose a simple NeweyWest type correction of the RV that yields an unbiased measure of volatility, and we characterize the optimal unbiased RV in terms of the mean squared error criterion. Our empirical analysis of the 30 stocks of the Dow Jones Industrial Average index shows the necessity of our general assumptions about the noise process. Further, the empirical results show that the modified RV is unbiased even if intraday returns are sampled every second. JEL Classification: C10; C22; C80.
Realized volatility: A review
 Econometric Reviews
, 2008
"... This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides ..."
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Cited by 12 (0 self)
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This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.
Asymptotic Theory for RangeBased Estimation of Integrated Variance of a Continuous SemiMartingale
, 2005
"... We provide a set of probabilistic laws for rangebased estimation of integrated variance of a continuous semimartingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for nonparametric measurement of return variation. Assuming the e ..."
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Cited by 12 (0 self)
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We provide a set of probabilistic laws for rangebased estimation of integrated variance of a continuous semimartingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for nonparametric measurement of return variation. Assuming the entire sample path realization of the logprice process is available and given weak technical conditions we prove that the highlow statistic converges in probability to the integrated variance. Moreover, with slightly stronger conditions, in particular a zero driftterm, we find an asymptotic distribution theory. To relax the meanzero constraint, we modify the estimator using an adjusted range. A weak law of large numbers and central limit theorem is then derived under more general assumptions about drift. In practice, inference about integrated variance is drawn from discretely sampled data. Here, we split the sampling period into subintervals containing the same number of price recordings and estimate the true range. In this setting, we also prove consistency and asymptotic normality. Finally, we analyze our framework in the presence of microstructure noise.
Finite sample accuracy of integrated volatility estimators. Working paper
, 2005
"... We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, the Fourier estimator, and the wavelet estimator, when a typical sample of highfrequency data is observed. We employ several different generating mechanisms for the instantaneous volatility p ..."
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Cited by 12 (1 self)
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We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, the Fourier estimator, and the wavelet estimator, when a typical sample of highfrequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. OrnsteinUhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using a model with bidask bounce in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bidask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias.