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 trade-off that serves as a basis for an optimal sampling theory. Our theory also considers the effects of pre-filtering the data and proposes a novel bias-correction. We show that this theory is easily implementable in practise requiring only the calculation of sample moments of the observable high-frequency return data.

We consider kernel-based 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 subsample-based estimator is closely related to a Bartlett-type 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 kernel-based estimators, which are also consistent. We study the efficiency of our new kernel-based procedure. We show that optimal modified kernel-based estimator converges to the integrated variance at rate m 1/4, where m is the number of intraday returns.

We develop an empirically highly accurate discrete-time 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 high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies 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 easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.

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 by-product 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 high-frequency data, and the theoretical works of Barndorff-Nielsen 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.

This paper motivates a reduced form discrete-time 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.

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.