Approximately optimal trade execution strategies under fast mean-reversion

Paper: arXiv 2307.07024

Authors: David Evangelista, Yuri Thamsten

Abstract

In a fixed time horizon, appropriately executing a large amount of a particular asset – meaning a considerable portion of the volume traded within this frame – is challenging. Especially for illiquid or even highly liquid but also highly volatile ones, the role of “market quality” is quite relevant in properly designing execution strategies. Here, we model it by considering uncertain volatility and liquidity; hence, moments of high or low price impact and risk vary randomly throughout the trading period. We work under the central assumption: although there are these uncertain variations, we assume they occur in a fast mean-reverting fashion. We thus employ singular perturbation arguments to study approximations to the optimal strategies in this framework. By using high-frequency data, we provide estimation methods for our model in face of microstructure noise, as well as numerically assess all of our results.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 6.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical framework applying singular perturbation theory and stochastic control to optimal execution under uncertain, fast mean-reverting liquidity and volatility. It balances high-level mathematical physics techniques with practical high-frequency data estimation methods and numerical experiments.

Research Flowchart

  flowchart TD
    A[Goal: Find optimal trade execution under uncertain, fast mean-reverting market quality] --> B[Inputs: High-Frequency Equity Data & Microstructure Noise]
    B --> C[Model Formulation: Price impact and volatility with fast mean-reverting stochastic variations]
    C --> D[Methodology: Singular Perturbation Analysis]
    D --> E[Computational Step: Parameter Estimation & Numerical Backtesting]
    E --> F[Outcomes: Robust, approximately optimal execution strategies & empirical validation]