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12
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 48 (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.
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 28 (5 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 20 (1 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.
“High Watermarks of Market Risks ” ♣
, 2007
"... The volatility has long been used as an auxiliary variable in the processes explaining the returns on risky assets. In this traditional framework, the observable were the returns and the volatility remained a latent variable, whose value or possible values were a byproduct of the estimation. Recent ..."
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The volatility has long been used as an auxiliary variable in the processes explaining the returns on risky assets. In this traditional framework, the observable were the returns and the volatility remained a latent variable, whose value or possible values were a byproduct of the estimation. Recently, the focus has changed and many studies have been devoted to empirical estimates of the volatility itself, without specifying necessarily any model for the prices themselves. This has been made possible by the increased availability of highfrequency data, and the theoretical works of BarndorffNielsen and Shephard (2002) showing convergence between an empirical measure of volatility and its theoretical expression. The empirical measure of volatility has been progressively refined, from a simple sum of squared returns to more sophisticated measures taking into account microstructure biases (see for instance Oomen, 2005). In parallel, some theoretical developments have put back into focus the role of jumps. There are now procedures to disentangle the jump part of the empirical volatility from its regular fluctuations. Taking the volatility as a random variable in itself means studying its characteristics. It is well known that volatility dynamics are autoregressive but also that obviously its process is stationary. Given that, it is natural to look for the best fit for the distribution of the volatility, given that the theory yields several possible candidates. Of special interest is the estimation of the likelihood of the volatility peaks, which relies on Extreme Value Theory. In this article, we first present several estimates of measures of risk, using both high frequency data and lower frequency data.
Duration Model, Autoregressive Conditional
, 2008
"... This paper motivates a reduced form discretetime series approach that models realized volatility by using its separated components, continuous variation and variation due to jumps. For this purpose, I combine Engle and Russell’s (1998) autoregressive conditional duration (ACD) model applied to the ..."
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This paper motivates a reduced form discretetime series approach that models realized volatility by using its separated components, continuous variation and variation due to jumps. For this purpose, I combine Engle and Russell’s (1998) autoregressive conditional duration (ACD) model applied to the continuous and jump size variation with Hamilton and Jordà’s (2002) autoregressive conditional hazard (ACH) model applied to jump durations. Further, the paper develops and discusses a methodology to evaluate density and probability function forecasts of this model class. The successful model fit and the favorable point and density forecast results show that the approach proposed in this paper qualifies as a useful forecast model for daily return variation.
A Comparison of Estimators Daily Realised Volatility
"... This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin (1996), which allows for hete ..."
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This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin (1996), which allows for heteroscedasticity and timevarying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.
unknown title
, 2007
"... Scale invariant distribution and multifractality of volatility multipliers in stock markets ..."
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Scale invariant distribution and multifractality of volatility multipliers in stock markets
Scaling and memory in the return intervals of realized volatility
, 904
"... We perform return interval analysis of 1min realized volatility defined by the sum of absolute highfrequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive ..."
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We perform return interval analysis of 1min realized volatility defined by the sum of absolute highfrequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the KolmogorovSmirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodnessoffit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponentγ and the threshold q. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both shortterm and longterm memory exists in the return intervals of realized volatility.
Realized Variance and IID Market Microstructure Noise
, 2004
"... We analyze the properties of a biascorrected realized variance (RV) in the presence of iid market microstructure noise. The bias correction is based on the firstorder autocorrelation of intraday returns and we derive the optimal sampling frequency as defined by the mean squared error (MSE) criteri ..."
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We analyze the properties of a biascorrected realized variance (RV) in the presence of iid market microstructure noise. The bias correction is based on the firstorder autocorrelation of intraday returns and we derive the optimal sampling frequency as defined by the mean squared error (MSE) criterion. The biascorrected RV is benchmarked to the standard measure of RV and an empirical analysis shows that the former can reduce the MSE by 50%90%. Our empirical analysis also shows that the iid noise assumption does not hold in practice. While this need not affect the RVs that are based on lowfrequency intraday returns, it has important implications for those based on highfrequency returns.