Title: Universal features of price formation in financial markets: perspectives from Deep Learning,
Abstract: 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.