This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the...

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to...

We show that (electronic) designated market makers are not necessarily beneficial to the stock market during ash crashes. They actually consume liquidity when it is most needed, even if they are rewarded by the exchange to provide immediacy. This behavior exacerbates the transient price impact,...

We provide a set of probabilistic laws for range-based estimation of integrated variance of a continuous semi-martingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for non-parametric measurement of return variation. Assuming...

Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + sigma (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the...

Central limit theorem, quadratic variation, bipower variation

In this paper we present two new tests for the parametric form of the variance function in difusion processes dXt = b(t;Xt)+ó(t;Xt)dWt: Our approach is based on two stochastic processes of the integrated volatility. We prove weak convergence of these processes to centered processes whose...

We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower...

We consider a new class of estimators for volatility functionals in the setting of frequently observed It¯o diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence...

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