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27
Separating microstructure noise from volatility
, 2006
"... There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moment ..."
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Cited by 64 (5 self)
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There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatilitytiming trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.
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 49 (5 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.
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.
2005b) Comments: A selective overview of nonparametric methods in …nancial econometrics
 Statistical Science
"... Abstract. These comments concentrate on two issues arising from Fan’s overview. The first concerns the importance of finite sample estimation bias relative to the specification and discretization biases that are emphasized in Fan’s discussion. Past research and simulations given here both reveal tha ..."
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Cited by 6 (4 self)
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Abstract. These comments concentrate on two issues arising from Fan’s overview. The first concerns the importance of finite sample estimation bias relative to the specification and discretization biases that are emphasized in Fan’s discussion. Past research and simulations given here both reveal that finite sample effects can be more important than the other two effects when judged from either statistical or economic viewpoints. Second, we draw attention to a very different nonparametric technique that is based on computing an empirical version of the quadratic variation process. This technique is not mentioned by Fan but has many advantages and has accordingly attracted much recent attention in financial econometrics and empirical applications. Key words and phrases: Nonparametric method, continuous time models, financial time series, jackknife, realized volatility. 1.
Identifying the covariation between the diffusion parts and the cojumps given discrete observations. Working paper, Dipartimento di Matematica per le Decisioni, Universita degli Studi di Firenze
, 2007
"... In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the integrated covariation (the covariation between the two diffusion parts, indicated by IC) from the ..."
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Cited by 5 (0 self)
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In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the integrated covariation (the covariation between the two diffusion parts, indicated by IC) from the cojumps. This has important applications to multiple assets price modeling for forecasting, option pricing, risk and credit risk management. An approach commonly used to estimate IC is to take the sum of the cross products of the two processes increments; however this estimator can be highly ∗Dipartimento di Matematica per le Decisioni, Università degli Studi di Firenze
Long Memory versus Structural Breaks in Modeling and Forecasting Realized Volatility
"... We explore the possibility of structural breaks in the realized volatility with the observed longmemory property for the daily Deutschemark/Dollar, Yen/Dollar and Yen/Deutschemark spot exchange rate realized volatility. The paper finds that the structural breaks can partly explain the persistence o ..."
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Cited by 3 (0 self)
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We explore the possibility of structural breaks in the realized volatility with the observed longmemory property for the daily Deutschemark/Dollar, Yen/Dollar and Yen/Deutschemark spot exchange rate realized volatility. The paper finds that the structural breaks can partly explain the persistence of realized volatility. We propose a VARRVBreak model that provides a superior predictive ability compared to most of the forecasting models when the future break is known. With unknown break dates and sizes, we find that the VARRVI(d) long memory model, however, is a very robust forecasting method even when the true financial volatility series are generated by structural breaks.
Diffusion covariation and cojumps in bidimensional asset price processes with stochastic volatility and infinite activity Lévy jumps, arXiv.org
, 2007
"... In this paper we consider two processes driven by diffusions and jumps. The jump components are Lévy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the two diffusion parts and the cojumps. The detection of the ..."
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Cited by 2 (1 self)
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In this paper we consider two processes driven by diffusions and jumps. The jump components are Lévy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the two diffusion parts and the cojumps. The detection of the cojumps allows to gain insight in the dependence structure of the jump components and has important applications in finance. Our estimators are based on a threshold principle allowing to isolate the jumps. This work follows Gobbi and Mancini (2006) where the asymptotic normality for the estimator of the covariation, with convergence speed √ h, was obtained when the jump components have finite activity. Here we show that the speed is √ h only when the activity of the jump components is moderate. 1
Identifying the diffusion covariation and the cojumps given discrete observations”, Working paper
, 2006
"... In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the cojumps. A commonly used approach to estimate the diffu ..."
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Cited by 2 (1 self)
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In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the cojumps. A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; however this estimator can be highly biased in the presence of jump components, since it approaches the quadratic covariation containing also the cojumps. Our estimator is based on a threshold principle allowing to isolate the jumps. As a consequence we find an estimator which is consistent. In the case of finite activity jump components the estimator is also asymptotically Gaussian. We assess the performance of our estimator for finite samples on four different simulated models.
Spot volatility estimation for highfrequency data
 Statistics and Its Interface
, 2008
"... The availability of highfrequency intraday data allows us to accurately estimate stock volatility. This paper employs a bivariate diffusion to model the price and volatility of an asset and investigates kernel type estimators of spot volatility based on highfrequency return data. We establish both ..."
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Cited by 2 (0 self)
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The availability of highfrequency intraday data allows us to accurately estimate stock volatility. This paper employs a bivariate diffusion to model the price and volatility of an asset and investigates kernel type estimators of spot volatility based on highfrequency return data. We establish both pointwise and global asymptotic distributions for the estimators.
Estimating correlation from high, low, opening and closing prices
 Annals of Applied Probability
, 2008
"... In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce unbiased (or nearunbiased) estimators with substantially lowe ..."
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Cited by 1 (0 self)
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In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce unbiased (or nearunbiased) estimators with substantially lower variance than the simple open– close estimator. This paper tackles the more difficult task of estimating the correlation of two stocks based on the daily opening, closing, high and low prices of each. If we had access to the high and low values of some linear combination of the two log prices, then we could use the univariate results via polarization, but this is not data that is available. The actual problem is more challenging; we present an unbiased estimator which halves the variance. 1. Introduction. There