Unwinding Toxic Flow with Partial Information

TL;DR

This paper models a trading desk managing unobserved adverse order flow toxicity, deriving optimal strategies under partial information, and demonstrating minimal performance loss compared to full information scenarios.

Contribution

It introduces a novel stochastic control framework for trading with unobserved toxicity, providing explicit filtering and optimal strategies under partial observability.

Findings

Optimal trading strategies are derived for momentum and mean-reverting toxicity.

Performance gap between partial and full information is approximately 0.01%.

The model effectively manages unobserved adverse order flow toxicity.

Abstract

We consider a central trading desk which aggregates the inflow of clients' orders with unobserved toxicity, i.e. persistent adverse directionality. The desk chooses either to internalise the inflow or externalise it to the market in a cost effective manner. In this model, externalising the order flow creates both price impact costs and an additional market feedback reaction for the inflow of trades. The desk's objective is to maximise the daily trading P&L subject to end of the day inventory penalization. We formulate this setting as a partially observable stochastic control problem and solve it in two steps. First, we derive the filtered dynamics of the inventory and toxicity, projected to the observed filtration, which turns the stochastic control problem into a fully observed problem. Then we use a variational approach in order to derive the unique optimal trading strategy. We illustrate our results for various scenarios in which the desk is facing momentum and mean-reverting toxicity. Our implementation shows that the P&L performance gap between the partially observable problem and the full information case are of order $0.01\%$ in all tested scenarios.