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永续期货的自适应做市与对冲

文章 arXiv papers · 作者: Minmin Zeng et al.
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总结

本文为做市商手续费为零的永续期货市场提出理论控制框架。做市商选择买卖价差，并通过在两家交易所之间对冲来管理库存。该框架将盈亏分解为价差收益、逆向选择、库存持有成本、对冲摩擦和资金费敞口。研究在常数绝对风险厌恶效用下采用 Hamilton–Jacobi–Bellman 公式，并报告验证定理。

论文还描述了盈利状态条件、去中心化永续合约交易场所的进出场阈值、考虑资金费的跨交易所对冲、不确定性边际、回撤界限、杠杆限制、库存行为和多配对配置。数值分析通过图示呈现盈利与非盈利状态间的转换。这些是理论结果；摘要未提供数据、参数值、执行假设或实际收益证据。实际结果取决于模型中的费用、成交、资金费、逆向选择和对冲摩擦是否与真实交易场所相符。

核心观点

  • 做市商联合控制买卖价差，并管理跨交易所的库存对冲。
  • 盈亏分解为价差收入、逆向选择、库存成本、对冲摩擦和资金费敞口。
  • 控制问题在CARA效用下用 Hamilton–Jacobi–Bellman 方程表示。
  • 该框架分析盈利状态、对冲选择、杠杆限制、回撤界限和投资组合配置。
  • 数值图示呈现盈利与非盈利区域之间的变化，但摘要未证明实盘表现。

标签

永续合约做市市场微观结构风险管理交易执行投资组合构建
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# Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets


# Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets









We develop a rigorous theoretical framework for optimal market making in perpetual futures markets with zero maker fees. We model the market maker's problem as a stochastic optimal control problem on a filtered probability space, where the controls are adaptive bid-ask spreads and inventory hedging decisions across two exchanges. Our contributions include: (i) a PnL decomposition theorem separating revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure; (ii) the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem; (iii) High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula; (iv) analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds; (v) optimal cross-exchange hedging policies with funding rate dynamics and a hedge regime trichotomy; (vi) a robustness margin quantifying parameter uncertainty tolerance; (vii) exponential drawdown probability bounds and a universal APY-VaR identity; (viii) ergodic inventory distribution under optimal control with Bayesian adaptive estimation; (ix) Kelly-optimal leverage with ruin boundaries; and (x) multi-pair portfolio allocation with diversification saturation results. Numerical analysis with twenty-three figures reveals phase transitions between profitable and unprofitable regimes. Our framework unifies and extends the Avellaneda-Stoikov, Gueant-Lehalle-Fernandez-Tapia, and Glosten-Milgrom paradigms for modern decentralized venue microstructure.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。