Work Package N.1 will mainly focus on the econometric analysis of a new feature of high-frequency data, recently emphasized by the PI, Davide Pirino and Federico Bandi. As statistically documented in Bandi, Pirino and Renò (2017), henceforth BPR17, price paths of financial assets show an abnormally “sluggish” behavior, in the sense that they experience less frequent price updates than expected under the null hypothesis of a frictionless market. In this case, the evolution of the price is assumed to be driven by a Brownian semi-martingale. Such a lack of price updates, whose main fingerprint is the occurrence, during the trading day, of zero returns, has non-trivial economic implications. In fact, as suggested in BPR17, the presence of zero returns could be produced by the joint effect of asymmetric information, transaction costs and delays in the incorporation of the information flow into the assets’ prices.
The empirical and theoretical findings of BPR17 opened several research questions, which constitute the core of WP1. WP1 is composed of a theoretical and an empirical line of research. The theoretical line is devoted to the analysis of the “idle time” measure, introduced in BPR17, and in particular to its dynamic modelling, its linkage to economic theories of price formation, and its behavior in a multi-variate framework. It is indeed natural to investigate whether illiquidity frictions have a significant, and economically relevant, systematic component. The identification of this component can turn, via a multivariate extension of the micro-founded model of BPR17, into an efficient identification scheme of the systematic component of funding costs and of market liquidity, and hence into an empirical validation of the testable implications of price formation theories, as those proposed, for example, in Brunnermeier and Pedersen (2009). In particular, we aim at testing how funding liquidity and market liquidity mutually influence each other.
This line of research will also investigate the statistical properties of prices flatness with methods based on the econometrics of infill asymptotics. In particular, we propose to study continuous-time models of price staleness, complementing the existing discrete-time theory.
The main purpose is the definition and the consistent estimation of “spot price flatness” and of volatility of illiquidity. Finally, we will dedicate some effort to the estimation of agent-based models of price formation with illiquidity frictions. In the literature, these models are unavoidably formulated in such a way that the likelihood is not analytically tractable, so estimation must exploit alternative methods, such as indirect inference (Gourieroux et al., 1993). Besides, to identify the model parameters, we aim at using moments sampled at multiple frequencies, which brings the complication that the asymptotic distributions of the parameter estimators are not known in this case, and thus needs to be studied in a coherent and general econometric framework.
This line of research is thought to fill this theoretical gap, by providing the asymptotic distribution of the structural estimators of micro-founded models of price formation, in presence of sampling at multiple frequencies.
The empirical line of WP1 is aimed at discovering new stylized facts about zero returns in financial asset prices. From an empirical point of view, it is now fundamental to quantify how much staleness in financial prices is spurious, i.e. attributable to institutional features such as price rounding. It is also necessary to assess the relationship between genuine (i.e. in excess to spurious) price sluggishness on one side, and volume, volatility and transaction costs on the other side.
These empirical investigations are required to shed light on the interpretation of zero returns as an illiquidity measure: which dimension of illiquidity is more related with genuine price staleness?
 
From the analyses in BPR17, at least three testable implications can be derived in this direction.
1) Transaction volumes during zero returns should be statistically and significantly smaller than during the rest of the day, not only at ultra-high frequency but also when data are sampled, say, every five minutes.
2) The volatility of observed prices should increase linearly with the number of consecutive zero returns.
3) According to the micro-founded model in BPR17, transaction costs should be positively correlated with the incidence of zero returns.
 
In order to have a robust empirical assessment of these three hypotheses we will mainly exploit a large data set of NYSE equity stocks and/or of BEDOFIH (see below for a brief description of available data-sets). We will first establish which percentage, on average in the data, of zero returns is explained by price discreteness. This computation allows a precise estimate of the genuine component of staleness. Hence we plan to obtain intra-day patterns of average (across stocks) transaction volumes, volatilities and bid-ask spreads, conditioned on genuine staleness and at different sampling frequencies. This analysis will also be important for the other work packages.