[Paper Review] Strategic Execution in the Presence of an Uninformed Arbitrageur

Ciamac C. Moallemi, Beomsoo Park+1 more|ArXiv.org|Jan 19, 2008

Complex Systems and Time Series Analysis10 references13 citations

TL;DR

This paper formulates a dynamic game of optimal execution under asymmetric information, where a risk-neutral trader liquidates a large position while an uninformed arbitrageur learns the trader's position through price movements. The authors develop an algorithm to compute perfect Bayesian equilibrium strategies, showing that traders must balance price impact and information leakage—leading to non-uniform, adaptive trading patterns that significantly reduce execution costs compared to standard strategies.

ABSTRACT

We consider a trader who aims to liquidate a large position in the presence of an arbitrageur who hopes to profit from the trader's activity. The arbitrageur is uncertain about the trader's position and learns from observed price fluctuations. This is a dynamic game with asymmetric information. We present an algorithm for computing perfect Bayesian equilibrium behavior and conduct numerical experiments. Our results demonstrate that the trader's strategy differs significantly from one that would be optimal in the absence of the arbitrageur. In particular, the trader must balance the conflicting desires of minimizing price impact and minimizing information that is signaled through trading. Accounting for information signaling and the presence of strategic adversaries can greatly reduce execution costs.

Motivation & Objective

• To model optimal execution as a dynamic game with asymmetric information between a trader and an uninformed arbitrageur.
• To develop an algorithm for computing perfect Bayesian equilibrium (PBE) behavior in this game.
• To analyze how information signaling affects optimal trading strategies and execution costs.
• To demonstrate that strategic behavior in response to learning arbitrageurs leads to qualitatively different, more efficient trading policies.

Proposed method

• Formulate a linear permanent price impact model with discrete-time dynamics and risk-neutral agents.
• Model the trader’s private information (position size) and the arbitrageur’s belief updating via Bayesian inference.
• Develop a recursive algorithm to compute perfect Bayesian equilibrium strategies using Gaussian beliefs and linear policies.
• Derive equilibrium trading rules that are linear in the trader’s position, the arbitrageur’s position, and the arbitrageur’s belief about the trader’s position.
• Use a relative volume parameter ρ₀ to capture the magnitude of trader activity relative to market noise.
• Conduct numerical experiments to analyze equilibrium behavior across different values of ρ₀ and time horizons.

Experimental results

Research questions

• RQ1 How does the presence of a learning arbitrageur alter the optimal execution strategy for a large trader?
• RQ2 What is the structure of perfect Bayesian equilibrium in a dynamic game of asymmetric information involving a trader and an uninformed arbitrageur?
• RQ3 How do information signaling and price impact interact in determining optimal trade sequencing?
• RQ4 Under what conditions does the trader benefit from delaying trades to reduce information leakage?
• RQ5 How does the relative volume parameter ρ₀ affect the shape of equilibrium trading strategies?

Key findings

• The trader’s equilibrium strategy is linear in his own position, the arbitrageur’s position, and the arbitrageur’s belief about the trader’s position.
• When relative volume ρ₀ is low, the trader equipsartitions trades to minimize price impact, ignoring the arbitrageur.
• When ρ₀ is high, the trader concentrates trading near the end of the horizon to minimize information leakage.
• The arbitrageur’s strategy is linear in his own position and his belief about the trader’s position, reflecting his learning process.
• The presence of the arbitrageur induces a spill-over effect, where the trader’s strategic behavior affects the arbitrageur’s incentives and market dynamics.
• Perfect Bayesian equilibrium strategies lead to significant cost reductions compared to deterministic, non-strategic execution policies.