Learning the Limit Order Book: a comprehensive mix between stochastic and machine learning models for generation and prediction

The field of finance is an interesting field in which much research takes place. In particular, its sub-field of modeling the dynamics of order books is an interesting field, since it translates into modeling the behaviour of traders on the market. Most of the models proposed in this field can be divided into stochastic models or machine learning models. The problem with the former ones is that they often make assumptions that do not propagate to practical applications, while the problem with the latter is that the models are often incomprehensible, even though they yield good results. This work tries to combine both of those fields to maintain the transparency of stochastic models and the accuracy of machine learning models. We target the limit order book, which is a book used in financial markets to place orders for financial securities in. It is a challenge to both generate realistic order books and predict them as well, since the model should be able to understand the underlying dynamics of order books to do this. We present a deep-learning-based model that is able to generate order books, through the use of a generative adversarial network (GAN) like architecture, and is able to predict order books using a similar architecture for the generator. Our models are able to outperform traditional generative and predictive models in both instances, while it remains transparent in its calculation: it is still able to extract useful and interpretable features from the underlying data set. These features, like the probabilities for up or down movements, or stagnations, or the rates at which the variables within the order book move, can be used by traders or algorithms to make sense out of the predictions. Traders can, for example, ask themselves whether the extracted features are representative of the analyzed asset and can, through this question, build additional confidence in the model. Another use case could be to utilize those features as inputs to other models. To our knowledge, this is the first work that proposes a combination of a stochastic and machine learning model to learn the dynamics of the order book