A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high-frequency returns coupled with simple modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures, the present paper provides a practical and robust framework for non-parametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from non-jump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the non-jump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.

There are two variance components embedded in the returns constructed using high frequency asset prices: the time-varying 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 volatility-timing trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.

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.

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.

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We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the i.i.d. bootstrap and the wild bootstrap (WB) and prove their first-order asymptotic validity under general assumptions on the log-price process that allow for drift and leverage effects. We derive Edgeworth expansions in a simpler model that rules out these effects. The i.i.d. bootstrap provides a second-order asymptotic refinement when volatility is constant, but not otherwise. The WB yields a second-order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provide third-order asymptotic refinements. Both methods improve upon the first-order asymptotic theory in finite samples.

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel Q. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility is robust to the form of contamination Q. To push the limits of our result, we show what happens for some models that involve rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also the use to which the estimator of volatility will be put.

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.