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.

[1]  N. Shephard,et al.  Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics , 2004 .

[2]  Estimating Quadratic Variation Consistently in the Presence of Correlated Measurement Error , 2006 .

[3]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[4]  Jean Jacod,et al.  A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales , 2004 .

[5]  Jeremy H. Large.  Estimating Quadratic Variation When Quoted Prices Change by a Constant Increment , 2007 .

[6]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[7]  J. Griffin,et al.  Covariance Measurement in the Presence of Non-Synchronous Trading and Market Microstructure Noise , 2009 .

[8]  Roel C. A. Oomen,et al.  A New Test for Jumps in Asset Prices , 2005 .

[9]  Brian Wildsmith,et al.  What a Tale , 1987 .

[10]  L. Rogers,et al.  Estimating Variance From High, Low and Closing Prices , 1991 .

[11]  R. Oomen,et al.  Testing for Jumps When Asset Prices are Observed with Noise - A Swap Variance Approach , 2007 .

[12]  R. Oomen.  Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes , 2005 .

[13]  P. Protter.  Stochastic integration and differential equations , 1990 .

[14]  Yue Fang,et al.  Volatility modeling and estimation of high-frequency data with Gaussian noise , 1996 .

[15]  Yacine Ait-Sahalia,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[16]  N. Shephard,et al.  Econometric analysis of realized volatility and its use in estimating stochastic volatility models , 2002 .

[17]  N. Yoshida,et al.  On covariance estimation of non-synchronously observed diffusion processes , 2005 .

[18]  Yuri Kabanov,et al.  From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift , 2006 .

[19]  S. Delattre,et al.  A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors , 1997 .

[20]  Jean Jacod,et al.  Diffusions with measurement errors. I. Local Asymptotic Normality , 2001 .

[21]  George Tauchen,et al.  Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance , 2012 .

[22]  N. Shephard,et al.  Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation , 2005 .

[23]  P. Protter,et al.  Asymptotic error distributions for the Euler method for stochastic differential equations , 1998 .

[24]  Jean Jacod,et al.  On continuous conditional Gaussian martingales and stable convergence in law , 1997 .

[25]  David Aldous,et al.  On Mixing and Stability of Limit Theorems , 1978 .

[26]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[27]  D. Dijk,et al.  Measuring volatility with the realized range , 2006 .

[28]  Luca Benzoni,et al.  An Empirical Investigation of Continuous-Time Equity Return Models , 2001 .

[29]  Federico M. Bandi,et al.  Microstructure Noise, Realized Variance, and Optimal Sampling , 2008 .

[30]  N. Shephard,et al.  Subsampling Realised Kernels , 2007 .

[31]  Jurgen A. Doornik,et al.  Object-orientd matrix programming using OX , 1996 .

[32]  N. Shephard,et al.  Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise , 2006 .

[33]  Kim Christensen,et al.  Realized Range-Based Estimation of Integrated Variance , 2006 .

[34]  Mark Podolskij,et al.  Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps , 2007, 0909.0827.

[35]  Lan Zhang.  Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach , 2004, math/0411397.

[36]  Michael W. Brandt,et al.  Range-Based Estimation of Stochastic Volatility Models , 2001 .

[37]  Michael W. Brandt,et al.  A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations , 2002 .

[38]  Kim Christensen,et al.  Range-Based Estimation of Quadratic Variation , 2006 .

[39]  P. Hansen,et al.  Realized Variance and Market Microstructure Noise , 2005 .

[40]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[41]  Yacine Aït-Sahalia,et al.  Disentangling diffusion from jumps , 2004 .

[42]  Torben G. Andersen,et al.  Stochastic volatility , 2003 .

[43]  Jeffrey R. Russell,et al.  Separating Microstructure Noise from Volatility , 2004 .