Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach

By Lan Zhang. 2004

555 citations recorded by the source corpus.

With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The former (consistency) has been addressed heavily in the recent literature, however, the resulting estimator is not quite efficient. In Zhang, Mykland, Ait-Sahalia (2003), the best estimator converges to the true volatility only at the rate of n wedge{-1/6}. In this paper, we propose an estimator, the Multi-scale Realized Volatility (MSRV), which converges to the true volatility at the rate of n wedge{-1/4}, which is the best attainable. We have shown a central limit theorem for the MSRV estimator, which permits setting intervals for the true integrated volatility on the basis of MSRV.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c8f8b18b4e8e8d66178686d37304308356941fdf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

VOLATILITY AND COVARIATION ESTIMATION WHEN MICROSTRUCTURE NOISE AND TRADING TIMES ARE ENDOGENOUS (2012, background): “Both lead to a highly biased behavior of naı̈ve high-frequency covariation measures, see Hayashi and Yoshida (2005), Voev and Lunde (2007), and Zhang (2006b).”
Microstructure Noise in the Continuous Case: The Pre-Averaging Approach ∗ (2008, methodology): “There are currently three main approaches to estimation in the nonparametric case: linear combination of realised volatilities obtained by subsampling (Zhang et al. (2005), Zhang (2006)), and linear combination of autocovariances (Barndorff-Nielsen et al. (2006)).”
A Note on the Central Limit Theorem for Bipower Variation of General Functions. (2008, background): “It also appears implicitly in the two-and multiscale approach proposed by Zhang, Mykland & Ait-Sahalia (2005) and Zhang (2006).”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, unknown): “…central limit theorem of Podolskij and Vetter (2009a) to the jumpy setting (see Barndorff-Nielsen, Hansen, Lunde, and Shephard, 2008; Jacod, Li, Mykland, Podolskij, and Vetter, 2009; Zhang, Mykland, and A¨ıt-Sahalia, 2005; Zhang, 2006, for further work on noise-robust volatility estimation).”
Semi-Parametric Comparison of Stochastic Volatility Models using Realized Measures (2006, background): “…subsampled realized volatility proposed by Zhang et al. (2005) is a consistent estimator of integrated volatility when prices are contaminated by microstructure noise (see also related contributions by Zhang, 2004; Aït-Sahalia et al., 2005b; Barndorff-Nielsen, Hansen, Lunde and Shephard, 2005b).”
Are Volatility Estimators Robust with Respect to Modeling Assumptions (2007, unknown): “We make use of some of the notations from Zhang et al. [27]: Let G = {0 = t0, t1, t2, . . . , tn = T } be the grid that contains all the observation times.”
The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency (2011, methodology): “…Zhang et al. (2005), Multi-Scale Realized Volatility (MSRV), a modification of TSRV which achieves the best possible rate of convergence proposed by Zhang (2006), Realized Kernels (RK) by Barndorff-Nielsen et al. (2008a), the Pre-Averaging volatility estimator (PAV) by Jacod et al. (2009), and the…”
Spot volatility estimation for high-frequency data ∗ (2008, background): “…and Shephard (2006)], two-time scale realized volatility (TSRV) [Zhang et al. (2005)], multiple-time scale realized volatility (MSRV) [Zhang (2006)], wavelet realized volatility (WRV) [Fan and Wang (2007)], kernel realized volatility (KRV) ∗Jianqing Fan is Frederick Moore ’18…”
Realized Variance and Market Microstructure Noise (2006, methodology): “This term is of order O(N−1/3) if k is chosen to be proportional to N2/3, as was done by Zhang et al. (2005). It appears that Zhou may have considered k as fixed in his asymptotic analysis, because he referred to this estimator as being inconsistent (see Zhou 1998, p. 114). Therefore, the great virt”
REALIZED BETA GARCH: A MULTIVARIATE GARCH MODEL WITH REALIZED MEASURES OF VOLATILITY (2012, background): “…and Markov chain estimators have been proposed to deal with issues such as jumps and market microstructure frictions, see Barndorff-Nielsen and Shephard (2004b), Barndorff-Nielsen, Hansen, Lunde and Shephard (2008), Zhang (2006), Jacod et al. (2009), Hansen and Horel (2009) and references therein.”
Covariance measurement in the presence of non-synchronous trading and market microstructure noise (2011, unknown): “Zhang (2006) provides an analytic treatment of the RC estimator in a general framework that includes non-synchronous trading and microstructure noise, Hayashi and Yoshida (2006) study the joint distribution of HY covariance estimator and RV in the absence of noise, Corsi (2006) studies the HY…”
Testing for Jumps When Asset Prices are Observed with Noise - A Swap Variance Approach (2008, unknown): “…Russell (2006), Barndorff-Nielsen, Hansen, Lunde, and Shephard (2006), Christensen, Podolskij, and Vetter (2006), Large (2005), Oomen (2005, 2006b), Zhang (2006), Zhang, Mykland, and Aı̈t-Sahalia (2005), Zhou (1996). swap variance jump test is that it can be applied, in analytically modified…”
Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error (2008, methodology): “Our estimator of QVX makes use of the same principles as the TSRV estimator in Zhang et al. (2005a).We split the original sample of size n into K subsamples, with the jth subsample containing nj observations. Introduce a constant β and c such that K = cn . The dependence of K on n is suppressed in t”
Econometrics of co-jumps in high-frequency data with noise (2015, background): “Several approaches have been invented, prominent ones by Zhang (2006), Barndorff-Nielsen et al. (2008), Jacod et al. (2009) and Xiu (2010) in the one-dimensional setting and generalizations for a noisy non-synchronous multi-dimensional setting by Aı̈t-Sahalia et al. (2010), Barndorff-Nielsen et al.…”
FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA (2013, methodology): “838 c© Cambridge University Press 2013 To the best of our knowledge, Wang and Zou (2010) is the first to propose a consistent estimator for large integrated volatility matrices using high-frequency data, allowing for both the number of assets and the sample sizes to go to infinity.”