Work Package N.2 is dedicated to the theoretical study of flash crashes, and in general of crashes in financial markets. WP2 will develop starting from the preliminary analysis of Christensen, Oomen and Renò (2017) and the concept of “Drift Burst Hypothesis”.
This working paper shows that the usual tenet that, for a semi-martingale, volatility dominates the returns dynamics at the highest frequencies is correct if the drift and volatility coefficients are bounded, but not necessarily true if the drift coefficient diverges at a suitable rate. Indeed, the financial literature has overlooked the possibility of drift explosions, which is instead theoretically sound and empirically relevant, as witnessed by the abrupt Flash Crash of May, 2010. What could lead to the explosion of the drift?
Huang and Wang (2009) show that endogenous order imbalances can originate from costly market presence and lead to market crashes. The effect can also propagate to other assets, as shown by Cespa and Foucault (2014). In the paper by Christensen et al. (2014), it is shown that almost all alleged jumps in financial prices are actually temporary crashes when looked at higher frequencies. WP2 aims at performing a thorough econometric analysis of the drift burst hypothesis. A robust test for drift burst will be introduced to detect flash crashes and gradual jumps, and disentangle them from other typical, but econometrically different, turmoil signals, such as volatility bursts and discontinuous jumps. Methodologically, the test builds on localized nonparametric estimators similar to those employed for the estimate of spot volatility, a field in which the PI contributed recently (see e.g Mancini, Mattiussi and Renò, 2015).
The proposed test can be implemented in real time and can be hugely important for market makers since it signals the ongoing liquidity evaporation. During a liquidity crash, traders can decide to pay an illiquidity risk premium to liquidity providers (Grossman and Miller, 1988).
The magnitude and size of the drift burst can then be used to understand the mechanics of the liquidity premium in distressed situations. Preliminary analysis on the BEDOFIH data set shows that drift burst appear as a temporary liquidity crash, as predicted by the papers quoted above, caused by abrupt large selling. WP1 has several theoretical and empirical aims.
 
In particular, we plan:
1) to introduce and study a semi-martingale model of drift bursts in the framework of the theory of stochastic differential equations with discontinuities and market microstructure noise;
2) to introduce a statistics, based on pre-averaged local estimators of drift and volatility (see, e.g., Jacod et al, 2009, Kristensen, 2010 and Mancini et al., 2015 and the discussion below) to identify these events in the data and disentangle them from bursts of volatility and jumps;
3) study a theoretical model of price formation which can generate drift bursts and spillovers, in order to provide a rational explanations to phenomena similar to the Flash Crash.
 
Once the theory is completed, this can be used for applications to the data to quantify the likelihood of drift burst events. This part of the project is totally new for the literature; it aims at introducing an unprecedented stylized fact for asset returns which brings relevant information about liquidity crashes, liquidity spillovers and systemic risk; finally, it is the basis for the implementation of a real-time indicator of flash crashes. Thus, results of WP2 are important for the other work packages.