Liquidity Commonality Does Not Imply Liquidity Resilience Commonality: A Functional Characterisation for Ultra-High Frequency Cross-Sectional LOB Data
37 Pages Posted: 5 Jun 2017
Date Written: June 23, 2014
We present a large-scale study of commonality in liquidity and resilience across assets in an ultra high-frequency (millisecond-time stamped) 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 proposed by [PPDZ14] for 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 crosssection 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.
Keywords: Limit Order Book, Liquidity, High Frequency Finance
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