Fuzzy representation of a limit order book as a measure of stock liquidity

Abstract

In this paper, we seek to ascertain whether the recently developed ordered fuzzy number (OFN) representation of a limit order book (LOB) by Marszałek and Burczyński (2024) may serve as a measure of stock liquidity. In particular, we aim to test whether this measure contains similar or distinct information than other stock liquidity measures, particularly relying only on best buy and sell orders. To this end, we have investigated the data on 259 companies in total over an eight-year period from 2014 to 2021. In total, we have compared the tested measure with eight different measures derived from the LOB data, all of which are computed on a weekly basis. Our results indicate that the OFN representation of a LOB correlates with other liquidity measures in the time series but is less correlated with them in the cross-section. Furthermore, it contains a distinct piece of information compared to the other measures, suggesting that it may capture a different liquidity dimension. In summary, the findings of the study suggest that the OFN representation of a LOB could serve as a measure of stock liquidity, particularly for large-volume trades and stocks with shallow or fragmented order books.