Universal features of price formation in financial markets: perspectives from Deep Learning

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model exhibits a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific. The universal model -- trained on data from all stocks -- outperforms, in terms of out-of-sample prediction accuracy, asset-specific linear and nonlinear models trained on time series of any given stock, showing that the universal nature of price formation weighs in favour of pooling together financial data from various stocks, rather than designing asset-or sector-specific models as commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations improves forecasting performance, showing evidence of path-dependence in price dynamics. The authors thank seminar participants at the London Quant Summit 2018, JP Morgan and Princeton University for their comments. Computations for this paper were performed using a grant from the CFM-Imperial Institute of Quantitative Finance and the Blue Waters supercomputer grant "Distributed Learning with Neural Networks". This data may be put to use to explore the nature of the price formation mechanism which describes how market prices react to fluctuations in supply and demand. At a high level, a'price formation mechanism' is a map which represents the correspondence between the market price and variables such as price history and order flow: Price(t t) F ( Price history(0...t), Order Flow(0...t), Other Information) F (X t, t), where X t is a set of state variables (e.g., lagged values of price, volatility, and order flow), endowed with some dynamics and t is a random'noise' or innovation term representing the arrival of new information and other effects not captured entirely by the state variables.