Paper: arXiv 2605.06405

Authors: Nam Anh Le

Abstract

This paper studies optimal liquidity provision for perpetual contracts when the funding rate is a stochastic state variable. The core extension to classical market making is the coupling between inventory and funding payments: inventory creates both mark-to-market exposure and a state-dependent funding cash flow. A reduced inventory-funding control problem is formulated, solved with a monotone finite-difference Hamilton-Jacobi-Bellman scheme, and bid and ask quote offsets are recovered from discrete inventory value differences. Funding is calibrated on Hyperliquid ETH, BTC, and SOL perpetual data. Gaussian OU funding is retained as a tractable diffusion baseline, while OU-plus-jump diagnostics document the heavy-tailed funding innovations that should enter a future extension. In 100-seed holdout simulations under two official-fill proxy calibrations, the funding-aware HJB improves mean ETH/BTC performance while lowering inventory RMS relative to classical Avellaneda-Stoikov. SOL gains are positive versus unscaled AS but are not a Pareto improvement once a risk-scaled AS diagnostic is included.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical framework by incorporating stochastic funding rates into optimal control (HJB) for perpetual DEX market making, supported by realistic finite-difference numerical methods. The empirical work is rigorous, using high-frequency DEX data and multi-seed holdout simulations that highlight practical performance trade-offs against benchmark models.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimal Market Making<br/>for Perpetual DEXs with Funding Rates"] --> B["Data & Calibration:<br/>Hyperliquid ETH, BTC, SOL Data<br/>(OU & OU-plus-Jump Processes)"]
    B --> C["Model Formulation:<br/>Coupled Inventory-Funding Stochastic Control<br/>(Mark-to-Market + Cash Flow Exposure)"]
    C --> D["Numerical Solution:<br/>Monotone Finite-Difference HJB Scheme<br/>to Recover Bid/Ask Offsets"]
    D --> E["Simulation & Evaluation:<br/>100-Seed Holdout Runs vs.<br/>Avellaneda-Stoikov Baselines"]
    E --> F["Outcomes:<br/>Improved Mean PnL & Lower Inventory RMS for ETH/BTC;<br/>Documented Heavy-Tailed Funding Innovations"]

Cited References (43)

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and 35 more
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5 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.