Paper: arXiv 2404.18200

Authors: Xue Cheng, Meng Wang, Ziyi Xu

Abstract

The interactions between a large population of high-frequency traders (HFTs) and a large trader (LT) who executes a certain amount of assets at discrete time points are studied. HFTs are faster in the sense that they trade continuously and predict the transactions of LT. A jump process is applied to model the transition of HFTs’ attitudes towards inventories and the equilibrium is solved through the mean field game approach. When the crowd of HFTs is averse to running (ending) inventories, they first take then supply liquidity at each transaction of LT (throughout the whole execution period). Inventory-averse HFTs lower LT’s costs if the market temporary impact is relatively large to the permanent one. What’s more, the repeated liquidity consuming-supplying behavior of HFTs makes LT’s optimal strategy close to uniform trading.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework using Mean Field Games and jump processes to model anticipatory high-frequency trading around a large trader. However, it is purely theoretical with no empirical data analysis or backtesting validation provided in the abstract and core setup.

Research Flowchart

  flowchart TD
    A[Research Goal: Model HFTs & Large Trader interactions using MFG] --> B[Inputs: Discrete LT execution, Inventory attitudes, Jump process]
    B --> C[Methodology: Solve Mean Field Game Equilibrium]
    C --> D[Compute Optimal HFT Inventory & Trading Dynamics]
    D --> E[Outcome 1: HFTs take then supply liquidity around LT trades]
    D --> F[Outcome 2: HFTs lower LT costs if temporary impact > permanent impact]
    D --> G[Outcome 3: HFT behavior pushes LT strategy toward uniform trading]

Cited References (47)

  1. Continuous auctions and insider trading (1985)
  2. Fast and slow informed trading (2019)
  3. Do high-frequency traders anticipate buying and selling pressure? (2021)
  4. The Flash Crash: High Frequency Trading in an Electronic Market (2017)
  5. Trading anonymity and order anticipation (2014)
  6. Order exposure and parasitic traders (1997)
  7. High frequency trading with speed hierarchies (2018)
  8. High-frequency trading around large institutional orders (2019)
and 39 more
  1. Predatory trading: a game on volatility and liquidity (2011)
  2. Liquidation in the face of adversity: stealth vs. sunshine trading (2009)
  3. Market liquidity: theory, evidence, and policy (2013)
  4. Front-Running and Market Quality: An Evolutionary Perspective on High Frequency Trading (2018)
  5. Equity trading in the 21st century (2011)
  6. Front-running dynamics (2008)
  7. Predatory trading (2005)
  8. Do short sellers front-run insider sales? (2013)
  9. Front-running scalping strategies and market manipulation: Why does high-frequency trading need stricter regulation? (2016)
  10. Back-running: Seeking and hiding fundamental information in order flows (2020)
  11. High-frequency trading and the execution costs of institutional investors (2014)
  12. Liquidity and information in limit order markets (2020)
  13. The economics of high-frequency trading: Taking stock (2016)
  14. Liquidity, resiliency and market quality around predictable trades: Theory and evidence (2016)
  15. No-dynamic-arbitrage and market impact (2010)
  16. News trading and speed (2016)
  17. High-frequency trading and market performance (2020)
  18. Informed trading when information becomes stale (2004)
  19. Are Large Traders Harmed by Front-running HFTs? (2023)
  20. The Effects of High-frequency Anticipatory Trading: Small Informed Trader vs. Round-Tripper — → 2304.13985
  21. Episodic liquidity crises: Cooperative and predatory trading (2007)
  22. Mean-field game strategies for optimal execution (2019)
  23. Mean field game of controls and an application to trade crowding (2018)
  24. Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis and Computation (2007)
  25. Fast and slow optimal trading with exogenous information (2022) — link
  26. Continuous-Time Mean Field Games with Finite State Space and Common Noise (2021)
  27. High-frequency market making to large institutional trades (2019)
  28. Order anticipation around predictable trades (2020)
  29. Concept Release on Equity Market Structure (2010)
  30. Mean field games (2007)
  31. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle (2006)
  32. Probabilistic Analysis of Mean-Field Games (2013)
  33. Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle (2010)
  34. $\epsilon$-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents (2013)
  35. Continuous time finite state mean field games (2013)
  36. Probabilistic Theory of Mean Field Games with Applications I-II (2018)
  37. Mean field and n-agent games for optimal investment under relative performance criteria (2019)
  38. Many-player games of optimal consumption and investment under relative performance criteria (2020)
  39. Mean-field games with differing beliefs for algorithmic trading (2020)

1 of 47 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.