Deep Learning to Estimate Expected Shortfall in Limit Order Books
Explore how leveraging deep learning algorithms like Probabilistic Neural Networks can revolutionize Expected Shortfall estimation in Limit Order Books.

Deep Learning to Estimate Expected Shortfall in Limit Order Books: A Game-Changer


Estimating expected shortfall (ES) has become increasingly important in the financial markets. Traditional methods often fall short when applied to Limit Order Books (LOBs). This article delves into a novel deep learning approach that surpasses the industry-standard GARCH models in accurately estimating ES tailored to LOBs.


In the world of finance, understanding the risk of losses due to market fluctuations is crucial. Limit Order Books (LOBs), which capture all resting limit orders of a specific exchange, have emerged as a high-dimensional, complex data source for such assessments. While Value-at-Risk (VaR) is commonly used to gauge market risk, it's far from perfect. Hence, the focus has shifted to Expected Shortfall (ES) as a more reliable risk measure.

The Need for New Approaches

Traditional methods to estimate ES are broadly classified into parametric, semi-parametric, and non-parametric models. While these approaches have their merits, none are perfectly suited for the complexities introduced by LOBs. This gap indicates a dire need for specialized models that consider LOB’s unique market microstructure.

Our Solution: A Deep Learning Model

Our approach employs a probabilistic neural network (PNN) specially designed for LOBs. It consists of three input channels to process millisecond, minutely aggregated, and spatial information. The model outperforms standard GARCH models and provides a new tool for financial practitioners, regulators, and traders.

Key Contributions

1. Novel ES Estimation Technique: Our model incorporates the unique characteristics of LOBs, capturing their spatio-temporal properties.
2. Risk Driver Analysis: We offer an analysis of the contributing risk factors in LOBs, emphasizing the significance of millisecond-level information.

Data and Methods

We utilized a subset of the daily Trade and Quote (TAQ) dataset tracking trades on NYSE, Nasdaq, and US regional exchanges. The data was split into training, evaluation, and holdout sets. Our PNN was trained using this dataset, with the architecture designed to capture temporal data at millisecond and minute levels.

Concluding Remarks

Our deep learning approach offers a superior alternative to existing models for estimating ES in financial markets. It is particularly useful for LOBs but can be adapted for various applications where spatio-temporal data is essential.