In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index $\theta$ of an EVaR is the relative cost of the expected margin shortfall and hence...

Finding a precise variance-covariance matrix is the building block of empirical finance. While microstructure-noise-robust methods for realized volatility are in the mainstream of financial econometrics, little if any attention has been devoted to estimating a noise-free realized covariance for...

In this paper we consider properties of random aggregation in time series analysis. For application, we focus on the problem of estimating high-frequency beta of an asset return when the returns are subject to the effects of market microstructure. Specifically, we study the correlation between...

The square-root-of-time rule (SRTR) is popular in assessing multi-period VaR; however, it makes several unrealistic assumptions. We examine and reconcile different stylized factors in returns that contribute to the SRTR scaling distortions. In complementing the use of the variance ratio test, we...

This paper offers a new and easy-to-implement projection-based approach to the identification of integrated volatility under the contamination from market microstructure noises. In stead of the typical two stage bias correction or optimal sampling procedure, we demonstrate that a precise...