Paper: arXiv 2409.12776

Authors: Luca Lalor, Anatoliy Swishchuk

Abstract

This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of the limit order book (LOB) dynamics within a scaling-limit framework. Given that algorithmic and HFT strategies now dominate major financial markets, accurately modeling LOB dynamics is crucial for developing effective trading algorithms. Recent research has shown that LOB data often exhibit non-Markovian properties, reinforcing the need for models that better capture its evolution. In this paper, we address acquisition and liquidation problems under more general compound semi-Markov and Hawkes jump-diffusion models. We first develop jump-diffusion frameworks to capture these dynamics and then apply diffusion approximations to the jump components so that robust solutions can be given. Optimal trading strategies are formulated using stochastic optimal control (SOC) and solved numerically. Finally, we present strategy simulations analyzing price paths, inventory evolution, trading speed, and average execution prices. This study provides insights into how these models can improve execution strategies under more general price dynamics.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous theoretical framework combining Semi-Markov and Hawkes jump-diffusions with stochastic optimal control for HFT execution problems. It provides solid mathematical derivations via scaling limit approximations and complements the theory with numerical simulations and real data calibrations.

Research Flowchart

  flowchart TD
    A[Goal: Optimize HFT Acquisition & Liquidation Strategies] --> B[Data Inputs: Non-Markovian Limit Order Book Dynamics]
    B --> C[Model Formulation: Semi-Markov & Hawkes Jump-Diffusion]
    C --> D[Methodology: Apply Diffusion Approximations to Jump Components]
    D --> E[Control Problem: Stochastic Optimal Control & Hamilton-Jacobi-Bellman]
    E --> F[Execution: Numerical Solution & Strategy Simulations]
    F --> G[Outcomes: Optimal Price Paths, Inventory Evolution & Execution Prices]

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6 of 98 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.