General Compound Hawkes Processes for Mid-Price Prediction

Abstract: High frequency financial data is burdened by a level of randomness that is unavoidable and obfuscates the task of modelling. This idea is reflected in the intraday evolution of limit orders book data for many financial assets and suggests several justifications for the use of stochastic models. For instance, the arbitrary distribution of inter arrival times and the subsequent dependence structure between consecutive book events. This has lead to the development of many stochastic models for the dynamics of limit order books. In this paper we look to examine the adaptability of one family of such models, the General Compound Hawkes Process (GCHP) models, to new data and new tasks. We further focus on the prediction problem for the mid-price within a limit order book and the practical applications of these stochastic models, which is the main contribution of this paper. To this end we examine the use of the GCHP for predicting the direction and volatility of futures and stock data and discuss possible extensions of the model to help improve its predictive capabilities.