https://grdm.io/tags/quant-finance/Recent content in Quant-Finance on Gerardo Duran-MartinHugoen-usWed, 11 Feb 2026 00:00:00 +0000https://grdm.io/articles/toxicflow2023/Wed, 11 Feb 2026 00:00:00 +0000https://grdm.io/articles/toxicflow2023/<h2 id="abstract">Abstract</h2> <p>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 statistically-efficient 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.</p>