Causal Survival Analysis in Limit Order Books: Estimation Fill Probabilities

Limit order books (LOB) are integral components of modern financial markets, providing a detailed record of buy and sell orders at various price levels for a given security. This research introduces a novel approach to analysing limit order books through causal inference. Traditional survival analysis, used for estimating how long a limit order will take to fill in the (LOB), encounters challenges due to the non-linear dynamics and macroeconomic factors influencing the complex environment of financial markets.

This esearch integrates causal inference methods with survival analysis, enhancing the understanding of financial market dynamics. The goal is to achieve a dual benefit: to gain deeper insights into the underlying mechanisms of market behaviour for improving the precision of estimation and to enable simulation of responses to macroeconomic changes and regulations.

In research, Causal Inference methods like Granger Causality, Peter-Clark Momentary Conditional Independence method and Attention-Based Convolutional Neural Networks explore how incoming orders, limit order book characteristics, and macroeconomic factors are interlinked. Causal Discovery uses statistical tests to identify potential correlations, lead-lag dynamics, and confounders, forming Directed Acyclic Graphs.

Then, a structural equation model is developed for order Fill Probability, assigning weights and dependencies to features linked to the target probability. When fitting survival models like Cox's proportional hazard model or any parametric survival model, these dependencies are restricted for feature engineering and coefficients. Proper scoring rules are used to compare the proposed method with classic and novel approaches in survival analysis.

To evaluate hypothetical scenarios and the causal effects of external shocks, regulations or macroeconomic announcements like federal rate hikes, counterfactual methodologies such as the Potential Outcomes Framework, do-calculus, and the Difference-in- Differences approach are employed. The four-year project begins with a comprehensive literature review and applying causal inference to the LOBSTER dataset.

The second year integrates causal inference with survival analysis. The third year focuses on counterfactual modelling of external changes, and the fourth year explores regulatory approaches and compiles findings into a dissertation. This research enhances risk management by offering precise insights into order fill times, aiding in anticipation of market fluctuations. It seeks to improve market liquidity, identify flash crashes,

and develop optimal execution strategies to reduce trading costs for institutions such as treasuries, central banks, and wealth funds. Furthermore, it contributes to creating informed regulatory policies for government authorities, which is crucial in preventing extreme volatility and ensuring global financial market stability.