Non-Parametric Prediction of the Mid-Price Dynamics in a Limit Order Book

Abstract

Many securities markets are organized as double auctions where each incoming limit order --- i.e., an order to buy or sell at a specific price --- is stored in a data structure called the limit order book. A trade happens whenever a market order arrives --- i.e., an order to buy or sell at the best currently available price. This order flow is visible to every market participant in real time. We propose a novel non-parametric approach to short-term forecasting of the mid-price change in a limit order book (i.e., of the change in the average of the best offer and the best bid prices). We construct a state vector characterizing the order book at each time instant and compute a feature vector for each value of the state vector. The features get updated during the course of a trading day, as new order flow information arrives. We cluster similar states together so that each cluster has enough observations for reliable feature estimation. The feature vector of a cluster is the average of the feature vectors of its constituent states. Our prediction at every time instant during the trading day is based on the feature vector of the cluster observed at that time instant. The distinction of our approach from the previous ones is that it does not impose a restrictive parametric model. Implicit assumptions of our method are very mild. Initial experiments with real order book data from NYSE suggest that our algorithms show promise. We illustrate their usage in a practical application of executing a large trade.

Keywords: non-parametric regression, limit order books

JEL Classification: C12, C13, C14, G10