This paper examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one.

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This paper introduces new econometric tests to identify stochastic intensity jumps in high-frequency data. Our approach exploits the behavior of a time-varying stochastic intensity and allows us to assess how intensely stock market reacts to news. We describe the asymptotic properties of our test statistics, derive the associated central limit theorem and show in simulations that the tests have good size and reasonable power in finite-sample cases. Implementing our testing procedures on the S&P 500 exchange-traded fund data, we find strong evidence for the presence of intensity jumps surrounding the scheduled Federal Open Market Committee (FOMC) policy announcements. Intensity jumps occur very frequently, trigger sharp increases in realized volatility and arrive when differences in opinion among market participants are large at times of FOMC press releases. Unlike intensity jumps, volatility jumps fail to explain the variation in news-induced realized volatility.

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In this article, we derive a new and unique method of estimating quantile and quantile density function, which is based on moments of fractional order statistics. A comparison of the proposed estimators is made with existing popular nonparametric quantile and quantile density estimators, in terms of mean squared error (MSE) for censored and uncensored data. Recommendations for the choice of quantile and/or quantile density estimators are given.