Liquidity commonality does not imply liquidity resilience commonality: A functional characterisation for ultra-high frequency cross-sectional LOB data

TL;DR

This study investigates liquidity and resilience commonality in ultra-high-frequency equity data, revealing that traditional methods misrepresent these features and proposing novel analytical techniques for better understanding market dynamics.

Contribution

The paper introduces a new approach using Independent Component Analysis and functional data analysis to better characterize liquidity resilience and its commonality across assets.

Findings

Independent Component Analysis reduces higher-order dependencies in liquidity data

Liquidity resilience profiles vary significantly across assets and thresholds

Market factors explain 10-40% of resilience variation at low liquidity levels

Abstract

We present a large-scale study of commonality in liquidity and resilience across assets in an ultra high-frequency (millisecond-timestamped) Limit Order Book (LOB) dataset from a pan-European electronic equity trading facility. We first show that extant work in quantifying liquidity commonality through the degree of explanatory power of the dominant modes of variation of liquidity (extracted through Principal Component Analysis) fails to account for heavy tailed features in the data, thus producing potentially misleading results. We employ Independent Component Analysis, which both decorrelates the liquidity measures in the asset cross-section, but also reduces higher-order statistical dependencies. To measure commonality in liquidity resilience, we utilise a novel characterisation as the time required for return to a threshold liquidity level. This reflects a dimension of liquidity that is not captured by the majority of liquidity measures and has important ramifications for understanding supply and demand pressures for market makers in electronic exchanges, as well as regulators and HFTs. When the metric is mapped out across a range of thresholds, it produces the daily Liquidity Resilience Profile (LRP) for a given asset. This daily summary of liquidity resilience behaviour from the vast LOB dataset is then amenable to a functional data representation. This enables the comparison of liquidity resilience in the asset cross-section via functional linear sub-space decompositions and functional regression. The functional regression results presented here suggest that market factors for liquidity resilience (as extracted through functional principal components analysis) can explain between 10 and 40% of the variation in liquidity resilience at low liquidity thresholds, but are less explanatory at more extreme levels, where individual asset factors take effect.