Brokers and Informed Traders: Dealing with Toxic Flow and Extracting Trading Signals

Source abstract

Abstract. We derive optimal strategies for an informed trader and a broker. The broker streams bespoke quotes to the informed trader and to a noise trader, and also trades in the lit market. The flow of the noise trader is uninformative and the broker trades with the noise trader at a profit, on average. On the other hand, the informed trader has privileged information about the trend in the price of the asset, so the broker trades with the informed trader at a loss, on average. These losses are payment for toxic flow from which the broker tries to learn the trend signal. The signal is one of the key ingredients in the broker’s trading strategy to internalize (i.e., how much of the flow she keeps in her books), to externalize (i.e., how much she unwinds in a lit exchange), and to speculate in the lit market. We obtain explicit solutions to the control problems of both the informed trader and the broker. The broker’s dynamic strategy is a linear combination of four processes: the broker’s inventory, the informed trader’s inventory, the trend signal, and the uninformed trader’s rate of trading with the broker. We demonstrate the efficacy of the trading strategy of the broker in several scenarios and perform robustness analysis against misspecification of model parameters. We employ simulations to conclude that the strategy we derived outperforms current market practices.