Hierarchical Hidden Markov Model of High-Frequency Market Regimes using Trade Price and Limit Order Book Information

Abstract

Over the last fifty years financial markets have seen an enormous expansion and development both in size and variety. An industry that was once small and secluded has transformed into an essential part of today’s economy. Such changes should in part be attributed to substantial advances in computer technology. The latest allowed for a transition from face-to-face trading on organized exchanges to a distributed system of electronic markets with new mechanisms serving the purposes of efficiency, transparency and liquidity. In majority of cases this new trading system is driven by a double auction market mechanism, in which market participants submit buy and sell orders, aiming to strike a balance between certainty of execution and attractiveness of trade price. Generally, information about outstanding buy and sell orders is made available to market participants in the form of a limit order book. It has been suggested by multiple prior research that limit order books contain information that could be used to derive market sentiment and predict future price movement. In the current study we have presented ideas behind double auction market mechanism and have attempted to model run and reversal market regimes using a simple and intuitive Hierarchical Hidden Markov Model. We have proposed a statistical measure of the limit order book imbalance and have used it to build observation (feature) vector for our model. We have built Limit Order Book analyzer – the software tool that has become essential for data cleaning and validation, as well as extraction of feature vector components from the data. We have used the model on high frequency tick-by-tick trade and limit order book data from the Toronto Stock Exchange. We have performed the analysis of computational results; for this purpose we have used a sample of annualized returns of stocks which comprised the TSX60 index at the time of data collection; we have performed the comparative analysis of our results with a simple daily buy & hold trading strategy as well as results of the trade price and volume model presented in the prior research.