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.

• The paper demonstrates that LSTM networks outperform linear models in forecasting price moves by capturing complex, nonlinear market dependencies.
• It finds universal and stable price formation patterns across diverse stocks, signing a common structural behavior in electronic markets.
• The study confirms that incorporating extensive historical order book data enhances predictive accuracy, highlighting long-range path-dependence.

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

This paper investigates the application of deep learning techniques to uncover universal patterns in the price formation mechanism within electronic financial markets. Utilizing a comprehensive dataset of high-frequency market transactions for US equities, the authors present evidence supporting the existence of a universal and stationary relation between order flows in a limit order book and subsequent price changes. This work highlights the capability of deep learning models, notably using Long Short-Term Memory (LSTM) networks, to capture complex, nonlinear dependencies in market data, often missed by traditional linear modeling approaches.

Key Findings

1. Nonlinearity and Deep Learning Models: The research demonstrates that deep learning models significantly outperform linear models, such as Vector Autoregressive (VAR) models, in forecasting the direction of price moves. The nonlinear nature of deep neural networks enables them to capture more complex patterns in the dataset, which are essential for accurate predictions in high-frequency market environments.
2. Universality Across Assets: A notable finding is that a universal model, trained on a diverse set of stocks, consistently outperforms stock-specific models. This indicates the presence of common structural patterns in the data that are independent of the specific asset. This generalization capability is further underscored by the model's robust performance on stocks not included in the training set, suggesting that the patterns learned are indeed universal across various financial instruments.
3. Temporal Stability: The authors present compelling evidence for the stationarity of the discovered patterns over time. The model's forecasting accuracy remains stable, even when applied to data collected a year after the initial training period, challenging the prevalent belief in the financial community about the need for frequent model recalibration due to assumed non-stationary data behavior.
4. Path-Dependence in Price Dynamics: The inclusion of extensive historical data improves the model's predictive performance, highlighting long-range dependencies in price formation. LSTM networks, which inherently manage temporal sequences, display enhanced accuracy over feedforward networks, underscoring the significance of order book history in modeling price changes.

Implications

The paper's insights have profound implications for both the theoretical understanding and practical application of financial market models:

• Theoretical Implications: The evidence of a universal, stationary price formation mechanism suggests a reevaluation of current market microstructure theories, which often assume asset-specific and non-stationary relations. The findings advocate for models that incorporate nonlinear and path-dependent dynamics, which can more accurately reflect the complexity of financial markets.
• Practical Applications: On the practical side, the universal model offers a more efficient and scalable approach to financial modeling. By pooling data across multiple assets, the deep learning framework allows for richer data inputs, which can lead to better-trained models. This approach reduces the computational overhead associated with developing stock-specific models and offers robust insights into newly listed securities or those with limited historical data, addressing common challenges in quantitative finance.

Future Prospects in AI

The successful application of deep learning to high-frequency market data opens avenues for further exploration into more sophisticated architectures like Transformer networks, which could potentially capture even richer dependencies in financial time series. Additionally, integrating external data sources, such as news sentiment or macroeconomic indicators, with market order book dynamics could yield more comprehensive predictive models, enhancing decision-making in trading and risk management.

This work stands as a significant contribution to the growing body of research demonstrating the power of AI in financial markets, suggesting that future developments will likely explore more integrated, adaptive, and data-driven approaches to financial modeling.