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Ultra high frequency volatility estimation with dependent microstructure noise
"... We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for tha ..."
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Cited by 56 (10 self)
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We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.
Estimating Quadratic Variation when Quoted Prices Jump by a Constant Increment
"... For financial assets whose best quotes almost always change by jumping by one price tick (e.g. a penny), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It compares the number of alternations, where quotes jump back to their previous price, to the n ..."
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Cited by 12 (1 self)
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For financial assets whose best quotes almost always change by jumping by one price tick (e.g. a penny), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It compares the number of alternations, where quotes jump back to their previous price, to the number of other jumps. If quotes are found to exhibit “uncorrelated alternation”, the estimator is consistent in a limit theory where jumps are very frequent and small. This condition is checked across a range of markets, which is enlarged by suitably rounding prices. The estimator helps to forecast volatility. A multivariate extension and feasible asymptotic theory are developed.
Vast Volatility Matrix Estimation using High Frequency Data for Portfolio Selection
, 2010
"... Portfolio allocation with grossexposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al. (2008b). The required highdimensional volatility matrix can be estimated by using high frequency fina ..."
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Cited by 4 (1 self)
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Portfolio allocation with grossexposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al. (2008b). The required highdimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt to the local volatilities and local correlations among vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This paper studies the volatility matrix estimation using highdimensional highfrequency data from the perspective of portfolio selection. Specifically, we propose the use of “pairwiserefresh time ” and “allrefresh time ” methods proposed by BarndorffNielsen et al. (2008) for estimation of vast covariance matrix and compare their merits in the portfolio selection. We also establish the concentration inequalities of the estimates, which guarantee desirable properties of the estimated volatility matrix in vast asset allocation with gross exposure constraints. Extensive numerical studies are made via carefully designed simulations. Comparing with the methods based on low frequency daily data, our methods can capture the most recent trend of the time varying volatility and correlation, hence provide more accurate guidance for the portfolio allocation in the next time period. The advantage of using highfrequency data is significant in our simulation and empirical studies, which consist of 50 simulated assets and 30 constituent stocks of Dow Jones Industrial Average index.
Integrated volatility and roundoff error
, 2009
"... We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency n, with roundoff error αn, of a diffusion on a finite inter ..."
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Cited by 2 (0 self)
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We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency n, with roundoff error αn, of a diffusion on a finite interval. We give from this sample estimators for different forms of the integrated volatility of the asset. Our method is based on variational properties of the process associated with wavelet techniques. We prove that the accuracy of our estimation procedures is αn ∨n −1/2. Using compensated estimators, limit theorems are obtained.
Particle FilterBased OnLine Estimation of Spot Volatility with Nonlinear Market Microstructure Noise Models
, 2010
"... Summary. A new technique for the online estimation of spot volatility for highfrequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. We make a clear distinction between volatility ..."
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Summary. A new technique for the online estimation of spot volatility for highfrequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. We make a clear distinction between volatility per time unit and volatility per transaction and provide estimators for both. A new nonlinear market microstructure noise model is proposed that reproduces the major stylized facts of highfrequency data. A computationally efficient particle filter is used that allows for the approximation of the unknown efficient prices and, in combination with a recursive EM algorithm, for the estimation of the volatility curves. In addition, the estimators are improved by an online bias correction. We neither assume that the transaction times are equidistant nor do we use interpolated prices.
Rounding Errors and Volatility Estimation ∗
, 2012
"... Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the ..."
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Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the asymptotic behavior of the Realized Volatility (RV), which is commonly used as an estimator of the integrated volatility. We prove the convergence of the RV and scaled RV under different conditions on the rounding level and the number of observations. A biascorrected volatility estimator is proposed and an associated central limit theorem is shown. Simulation and empirical results show that the improvement in statistical properties can be substantial.
Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A LocaltoContinuity Theory for the Preaveraging Method ∗
, 2012
"... We develop an asymptotic theory for the preaveraging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics ..."
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We develop an asymptotic theory for the preaveraging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple biascorrected estimators for jump power variations, and construct robust confidence sets with valid asymptotic size in a uniform sense. The method is also robust to microstructure noise.