Limit order book fill probability
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Estimating Fill Probability in Limit Order Books
Introduction to Limit Order Books and Fill Probability
In financial markets, a limit order book (LOB) is a record of all outstanding limit orders in a market, organized by price level. Understanding the fill probability, or the likelihood that a limit order will be executed within a certain time frame, is crucial for traders deciding between market orders and limit orders. This article synthesizes recent research on estimating fill probabilities in LOBs using various modeling techniques.
Deep Learning Approaches to Fill Probability
Recurrent Neural Networks for Time-to-Fill Estimation
A recent study proposes a data-driven approach using recurrent neural networks (RNNs) to estimate the distribution of time-to-fill for limit orders based on current market conditions. This method has shown superior performance compared to traditional techniques and has led to significant cost reductions in trading strategies.
Convolutional-Transformers for Survival Analysis
Another innovative approach employs a convolutional-Transformer encoder combined with a monotonic neural network decoder to estimate fill times of limit orders. This method maps time-varying features of the LOB to the distribution of fill times and significantly outperforms traditional survival analysis techniques. The study also highlights the importance of understanding the informativeness of features used to compute fill probabilities.
Analytical Models of Limit Order Books
Queueing Theory and Order Book Depth
An analytical model based on queueing theory examines the relationship between the size of incoming limit orders and the shape of the order book. The model shows that fewer, larger limit orders result in a deeper order book around the spread. This relationship has been empirically tested on stocks traded on the Paris stock exchange, providing a theoretical foundation for understanding order book dynamics .
Hawkes Process for Order Arrivals
The Hawkes process, a type of self-exciting point process, has been used to model the flow of market orders, limit orders, and cancellations in LOBs. This model incorporates the 'limit-order-book imbalance' to explain the probability of a market order being executed. The imbalance is included in the baseline intensity of the process, allowing for the prediction of the next order type.
Practical Applications and Implications
Execution Probability Models
A computable execution probability model for limit order markets explores the effects of the lengths of both buy and sell queues on the execution probability. This model introduces the cumulative probability of limit orders as a crucial index of market depth, providing new insights into the structure of order placement decisions.
Generative Models for LOB Dynamics
Generative models based on recurrent neural networks have been developed to capture the complete dynamics of LOBs. These models decompose the probability of each transition into conditional probabilities of order type, price level, order size, and time delay. Such models have been successfully trained on both synthetic and real data, demonstrating their applicability in trading execution.
Conclusion
Estimating fill probabilities in limit order books is a complex but essential task for optimal trading strategies. Recent advancements in deep learning, particularly the use of RNNs and convolutional-Transformers, have significantly improved the accuracy of these estimates. Analytical models based on queueing theory and the Hawkes process provide a theoretical foundation for understanding order book dynamics. These approaches collectively enhance our ability to predict and optimize the execution of limit orders in financial markets.
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