Detecting toxic flow

Journal article

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statisticallyefficient Bayesian procedure for online training of neural networks. We employ a proprietary dataset of foreign exchange transactions to test our methodology. Neural networks trained with PULSE outperform standard machine learning and statistical methods when predicting if a trade will be toxic; the benchmark methods are logistic regression, random forests, and a recursively-updated maximum-likelihood estimator. We devise a strategy for the broker who uses toxicity predictions to internalise or to externalise each trade received from her clients. Our methodology can be implemented in real-time because it takes less than one millisecond to update parameters and make a prediction. Compared with the benchmarks, online learning of a neural network with PULSE attains the highest PnL and avoids the most losses by externalising toxic trades.

Authors: Cartea, Á; Duran-Martin, G; Sanchez Betancourt, LG

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Taylor & Francis
• Journal: Quantitative Finance
• Publication date: 2026-02-11
• Acceptance date: 2026-01-15
• DOI: 10.1080/14697688.2026.2619539
• EISSN: 1469-7696
• ISSN: 1469-7688
• Language: English
• Keywords: algorithmic trading; Bayesian neural networks; brokers; detection; toxic flow; Kalman filter; online learning