Optimal Execution with Identity Optionality

TL;DR

This paper models how anonymous and identified trading strategies affect optimal execution in financial markets, using mean-field game theory to derive closed-form solutions and analyze parameter sensitivities.

Contribution

It introduces a mean-field game framework for optimal execution considering identity optionality and derives explicit solutions within the Almgren-Chris impact model.

Findings

Closed-form solutions for optimal strategies under identity optionality.

Sensitivity of strategies to model parameters analyzed.

Impact of anonymous vs. identified trading on execution costs explored.

Abstract

This paper investigates the impact of anonymous trading on the agents' strategy in an optimal execution framework. It mainly explores the specificity of order attribution on the Toronto Stock Exchange, where brokers can choose to either trade with their own identity or under a generic anonymous code that is common to all the brokers. We formulate a stochastic differential game for the optimal execution problem of a population of $N$ brokers and incorporate permanent and temporary price impacts for both the identity-revealed and anonymous trading processes. We then formulate the limiting mean-field game of controls with common noise and obtain a solution in closed-form via the probabilistic approach for the Almgren-Chris price impact framework. Finally, we perform a sensitivity analysis to explore the impact of the model parameters on the optimal strategy.