Characterising order book evolution using self-organising maps

Trading on major financial markets is typically conducted via electronic order books whose state is visible to market participants in real-time. A significant research literature has emerged concerning order book evolution, focussing on characteristics of the order book such as the time series of trade prices, movements in the bid-ask spread and changes in the depth of the order book at each price point. The latter two items can be characterised as order book shape where the book is viewed as a histogram with the size of the bar at each price point corresponding to the volume of shares demanded or offered for sale at that price. Order book shape is of interest to market participants as it provides insight as to current, and potentially future, market liquidity. Questions such as what shapes are commonly observed in order books and whether order books transition between certain shape patterns over time are of evident interest from both a theoretical and practical standpoint. In this study, using high-frequency equity data from the London Stock Exchange, we apply an unsupervised clustering methodology to determine clusters of common order book shapes, and also attempt to assess the transition probabilities between these clusters. Findings indicate that order books for individual stocks display intraday seasonality, exhibit some common patterns, and that transitions between order book patterns over sequential time periods is not random.