Paper: arXiv 2310.14144

Abstract

We study how to unwind stochastic order flow with minimal transaction costs. Stochastic order flow arises, e.g., in the central risk book (CRB), a centralized trading desk that aggregates order flows within a financial institution. The desk can warehouse in-flow orders, ideally netting them against subsequent opposite orders (internalization), or route them to the market (externalization) and incur costs related to price impact and bid-ask spread. We model and solve this problem for a general class of in-flow processes, enabling us to study in detail how in-flow characteristics affect optimal strategy and core trading metrics. Our model allows for an analytic solution in semi-closed form and is readily implementable numerically. Compared with a standard execution problem where the order size is known upfront, the unwind strategy exhibits an additive adjustment for projected future in-flows. Its sign depends on the autocorrelation of orders; only truth-telling (martingale) flow is unwound myopically. In addition to analytic results, we present extensive simulations for different use cases and regimes, and introduce new metrics of practical interest.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated stochastic control model with analytic solutions and heavy use of advanced probability theory (martingales, dynamic programming, stochastic maximum principle), indicating high mathematical complexity. However, it focuses on theoretical modeling and simulation studies without presenting backtest-ready implementation, code, or real empirical data, placing it in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Optimal Unwind of Stochastic Order Flow<br>with Minimal Transaction Costs"] --> B["Methodology:<br>Modeling Stochastic In-Flow Process"]
  B --> C["Key Inputs:<br>Order Flow Characteristics<br>Market Microstructure Parameters"]
  C --> D["Computation:<br>Stochastic Optimal Control<br>Semi-Closed Form Solution"]
  D --> E["Core Analytic Finding:<br>Unwind Strategy = Base Execution<br>+ Additive Adjustment for Future Flows"]
  E --> F["Key Outcomes & Regimes:<br>• Truth-Telling Flow: Myopic Unwind<br>• Autocorrelation Sign Determines Strategy"]
  F --> G["Validation:<br>Multi-Asset Simulations &<br>New Practical Metrics"]