Tackling the Problem of State Dependent Execution Probability: Empirical Evidence and Order Placement

Order placement tactics play a crucial role in high-frequency trading algorithms and their design is based on understanding the dynamics of the order book. Using high quality high-frequency data and survival analysis, we exhibit strong state dependence properties of the fill probability function. We define a set of microstructure features and train a multi-layer perceptron to infer the fill probability function. A weighting method is applied to the loss function such that the model learns from censored data. By comparing numerical results obtained on both digital asset centralized exchanges (CEXs) and stock markets, we are able to analyze dissimilarities between the fill probability of small tick crypto pairs and large tick assets-large, relative to cryptos. The practical use of this model is illustrated with a fixed time horizon execution problem in which both the decision to post a limit order or to immediately execute and the optimal distance of placement are characterized. We discuss the importance of accurately estimating the clean-up cost that occurs in the case of a non-execution and we show it can be well approximated by a smooth function of market features. We finally assess the performance of our model with a backtesting approach that avoids the insertion of hypothetical orders and makes possible to test the order placement algorithm with orders that realistically impact the price formation process.