An Applicability-Aware Benchmark of Predictive Models for Paired-Leg Arbitrage

This paper investigates the reliability of statistical and machine-learning models for predicting execution outcomes in cross-venue arbitrage, where both trading legs may execute, only one may execute, or neither may execute. Ten predictive models, including Bayesian Dirichlet methods, logistic regression, random forests and gradient boosting, are evaluated across ten synthetic market environments, three training-sample sizes and five simulation replications, producing 1,500 fitted-model evaluations. Predictive performance is assessed using logarithmic loss, Brier scores, conditional Kullback–Leibler divergence and statistical tests of model superiority. The study also examines robustness to changing market conditions, including gradual drift, abrupt structural breaks and hidden market regimes. Quadratic multinomial logistic regression achieves the lowest pooled test log loss with 2,000 training observations (1.0383), although differences among the leading models are not statistically significant under the reported multiple-comparison tests. Results demonstrate that model effectiveness depends on market conditions, training-sample size and distributional assumptions. The research provides a reproducibility-oriented framework for evaluating probabilistic execution models and identifying their limitations. All experimental results are based on synthetic data and do not establish real-market trading profitability.