Recent literature on realized volatility suggests that the observed price process of an asset may be decomposed into two parts: the unobservable, efficient price process and microstructure noise. In this article we present a methodology to sequentially estimate spot volatility from noisy data by separating these components. We use different liquidity-based measures, traded volume and quoted spr...

In this paper minimax lower bounds are derived for the estimation of the instantaneous volatility in three related high-frequency statistical models. These bounds are based on new upper bounds for the Kullback-Leibler divergence between two multivariate normal random variables along with a spectral analysis of the processes. A comparison with known upper bounds shows that these lower bounds are...

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price...

A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved. The estimator is shown to be also robust to market microstructure noise induced by price discreteness and bid-ask spreads.

A procedure that enables the evaluation and further distillation of fixed pattern noise for digital capture devices is proposed. This method also allows for the direct calculation of the random, or temporal, noise contribution, devoid of fixed pattern components. Our method is consistent with a draft digital camera noise measurement standard under consideration through ISO 15739, but is intende...