In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing...

In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing...

This paper proposes one new stochastic approximation algorithm for solving simulation-based optimization problems. It employs a weighted combination of two independent current noisy gradient measurements as the iterative direction. It can be regarded as a stochastic approximation algorithm with...

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility -- in particular, it gives feasible ways to consistently estimate the asymptotic variance...

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...

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high-frequency data. The puzzle lies...

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of portfolios selection among a vast pool of assets, as demonstrated by Fan, Zhang, and Yu. The required high-dimensional volatility matrix can be estimated by using high-frequency...