Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning

20 Pages Posted: 16 Mar 2018 Last revised: 29 Mar 2018

Justin Sirignano

Imperial College London - Department of Mathematics; University of Illinois at Urbana-Champaign

Rama Cont

University of Oxford; CNRS

Date Written: March 16, 2018


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 is shown to exhibit 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 is shown to improve forecasting performance, showing evidence of path-dependence in price dynamics.

Keywords: Financial Econometrics, High Frequency Data, Machine Learning, Deep Learning, Price Formation, Market Microstructure, Intraday Data, Limit Order Book

JEL Classification: C14, C45, C58

Suggested Citation

Sirignano, Justin and Cont, Rama, Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning (March 16, 2018). Available at SSRN: https://ssrn.com/abstract=3141294 or http://dx.doi.org/10.2139/ssrn.3141294

Justin Sirignano

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
United Kingdom

HOME PAGE: http://jasirign.github.io

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Rama Cont (Contact Author)

University of Oxford ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

CNRS ( email )

Sorbonne University

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

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