Observed asset prices are known to deviate from their efficient values due to market microstructure frictions. This paper studies the effects of market microstructure noise on nonparametric estimates of the efficient price integrated variance. Specifically, we consider both asymptotic and finite sample effects of general market microstructure noise on realized variance estimates. The finite sample results culminate in a variance/bias trade-off that serves as a basis for an optimal sampling theory. Our theory also considers the effects of pre-filtering the data and proposes a novel bias-correction. We show that this theory is easily implementable in practise requiring only the calculation of sample moments of the observable high-frequency return data.

We study the finite sample properties of the Fourier estimator of integrated volatility under market microstructure noise. We derive an analytic expression for the bias and the mean squared error of the contaminated estimator. These estimates can be practically used to design optimal MSE-based estimators, which are very robust and efficient in the presence of noise. Moreover an empirical analysis based on a simulation study and on high-frequency logarithmic prices of the Italian stock index futures (FIB30) validates the theoretical results. JEL: C10,C13,C14,C15,C22

During the last decades a wide literature has focused on the relationship volumevolatility on financial markets. This paper investigates the temporal dynamics of volatility and volumes, supposing, as in Bollerslev and Jubinski (1999), that the link has to be found in their long-run dependencies, that are supposed to be driven by the same informative process. We analyze the volume-volatility relationship using IBM stocks data. In particular, we rely on the realized volatility based on five minutes stock prices. Tail dependence analysis is carried out with two alternative estimators of the continuous part of the volatility process. The analysis shows that log-realized volatility and logvolumes are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. We also investigate the possibility that volumes and volatility are driven by a common fractionally integrated stochastic trend, i.e. they have the same degree of long memory and are fractionally cointegrated as the Mixture Distribution Hypotesis prescribes. Moreover, we estimate a bivariate FIVAR specification that explicitly considers the long run relationship between the two series and the tail dependence in the shocks, by parameterizing the joint density by means of different copula functions. The evidence from the model estimates, the simulation results and the forecasts comparison with HAR model highlight the ability of the bivariate FIVAR with copula density specification to account for the common long memory pattern and tail dependence.

Abstract: We propose a method to estimate the intraday volatility of a stock by integrating the instantaneous conditional return variance per unit time obtained from the autoregressive conditional duration (ACD) models. We compare the daily volatilities estimated using the ACD models against several versions of the realized volatility (RV) method, including the bipower variation realized volatility with subsampling, the realized kernel estimate and the duration-based realized volatility. The ACD volatility estimates correlate highly with and perform very well against the RV estimates. Our Monte Carlo results show that our method has lower root mean-squared error than the RV methods in most cases. A clear advantage of our method is that it can be used to estimate intraday volatilities over intervals such as an hour or 15 minutes.

In this paper we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 futures. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high frequency intra-day returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analyzed.