Optimal Order Placement under a State-Dependent Hawkes Process Limit Order Book model

Paper: arXiv 2610.37324

Authors: Jonathan Chávez Casillas, Li Gan

Abstract

We study optimal quote placement for a market maker facing order flow modeled by a state-dependent Hawkes process. A block-based linear demand specification links market-order counts to execution volumes, providing the demand moments required by a continuous time discrete state dynamic programming formulation. Under a quadratic terminal inventory penalty, we characterize inventory-dependent quotes and derive backward recursions for the coefficients of a quadratic value function. Numerical experiments using LOBSTER data examine quote distributions, inventory exposure, and terminal wealth. The implemented strategy yields higher aggregate terminal wealth than fixed-spread benchmarks at one and three ticks, but lower wealth than the two-tick benchmark. These results illustrate the framework’s numerical implementation and distinguish terminal-wealth comparisons from evaluation under the inventory-penalized objective.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 7.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework for optimal order placement using state-dependent Hawkes processes, demonstrating strong empirical validation with LOBSTER data. The novelty lies in integrating sdHawkes processes into a stochastic optimal control framework for market making, which is a significant contribution. While the methodology is detailed, explicit code or data links for full reproducibility are not mentioned in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Quote Placement for Market Maker] --> B{Methodology: State-Dependent Hawkes Process + Dynamic Programming};
    B --> C[Model Inputs: LOBSTER Data, Block-based Linear Demand, Quadratic Terminal Inventory Penalty];
    C --> D{Computational Process: Backward Recursions for Quadratic Value Function Coefficients};
    D --> E[Key Findings: Inventory-Dependent Quotes Characterized];
    E --> F{Outcomes: Higher Aggregate Terminal Wealth vs. 1 & 3-Tick Fixed Spreads};
    F --> G[Further Outcome: Lower Wealth vs. 2-Tick Fixed Spread, illustrating objective differences];