Unwinding Toxic Flow with Partial Information

ArXiv ID: 2407.04510 “View on arXiv”

Authors: Unknown

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.

Keywords: stochastic control, order toxicity, price impact, partial observability, Kalman filtering, Equities (Market Microstructure)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents a complex stochastic control problem with partial observations, filtering theory, and variational methods, requiring advanced mathematics. While it includes a numerical simulation and references to FX flow data, it lacks extensive backtesting, code, or empirical validation typical of high-rigor implementations, focusing more on theoretical derivations.

  flowchart TD
    A["Research Goal"] --> B["Formulate Stochastic Control Problem"]
    B --> C["Apply Kalman Filtering for Partial Observability"]
    C --> D["Derive Fully Observed Equivalent Problem"]
    D --> E["Compute Optimal Strategy via Variational Approach"]
    E --> F["Simulate Scenarios<br/>Momentum vs Mean-Revert Toxicity"]
    F --> G{"Outcomes"}
    G --> H["P&L Performance Gap ~ 0.01%"]
    G --> I["Robust Optimal Strategy"]
    
    subgraph Inputs
        direction LR
        J["Client Order Inflow"] --> B
        K["Unobserved Toxicity"] --> B
        L["Inventory Constraints"] --> B
    end