TL;DR: Under this framework, it becomes clear why and where the “usual” volatility estimator fails when the returns are sampled at the highest frequencies, and a way of finding the optimal sampling frequency for any size of the noise.
Abstract: It is a common nancial practice to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenge to this estimation approach, as evidenced by recent empirical studies in nance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the \usual" volatility estimator fails when the returns are sampled at the highest frequency.
TL;DR: In this article, a consistent and efficient estimator of the high-frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise, is proposed.
Abstract: This article proposes a consistent and efficient estimator of the high-frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise. This estimator is built on the marriage of the quasi–maximum likelihood estimator of the quadratic variation and the proposed generalized synchronization scheme and thus is not influenced by the Epps effect. Moreover, the estimation procedure is free of tuning parameters or bandwidths and is readily implementable. Monte Carlo simulations show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods. The empirical studies of six foreign exchange future contracts illustrate the time-varying correlations of the currencies during the 2008 global financial crisis, demonstrating the similarities and differences in their roles as key currencies in the global market.
TL;DR: In this article, the authors show that the usual covariance estimator is biased and the size of the bias is more pronounced for less liquid assets, and provide optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization.
Abstract: This paper is about how to estimate the integrated covariance _T of two price processes over a fixed time horizon [0, T], when the observations about X and Y are contaminated and when such noisy observations are at discrete, but not synchronized, times. We show that the usual covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. We also provide optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization.
TL;DR: In this article, the Epps effect and the effect of microstructure noise are analyzed and a two-scale covariance estimator is provided which simultaneously cancels (to first order) the Eppes effect and other sources of stochastic error terms, including nonsynchronous trading, non-synchronized trading, and time discretization.
TL;DR: In this article, the authors investigated the high-frequency cross-correlation existing between pairs of stocks traded in a financial market and investigated the hierarchical organization of the investigated stocks by determining a metric distance between stocks and by investigating the properties of the subdominant ultrametric associated with it.
Abstract: The high-frequency cross-correlation existing between pairs of stocks traded in a financial market are investigated in a set of 100 stocks traded in US equity markets. A hierarchical organization of the investigated stocks is obtained by determining a metric distance between stocks and by investigating the properties of the subdominant ultrametric associated with it. A clear modification of the hierarchical organization of the set of stocks investigated is detected when the time horizon used to determine stock returns is changed. The hierarchical location of stocks of the energy sector is investigated as a function of the time horizon.