Adaptive Market Making and Hedging in Perpetual Futures
Summary
This paper proposes a theoretical control framework for market making in zero-maker-fee perpetual futures markets. A market maker chooses bid and ask spreads and manages inventory through hedging across two exchanges. The framework decomposes profit and loss into spread revenue, adverse selection, inventory carrying costs, hedging friction, and funding exposure. It uses a Hamilton–Jacobi–Bellman formulation under constant absolute risk aversion utility and reports a verification theorem.
The paper also describes profitable-regime conditions, entry and exit thresholds for decentralized perpetual venues, funding-aware cross-exchange hedging, uncertainty margins, drawdown bounds, leverage limits, inventory behavior, and multi-pair allocation. Numerical analysis is presented through figures showing transitions between profitable and unprofitable regimes. These are theoretical results; the abstract does not provide data, parameter values, execution assumptions, or evidence of realized returns. Practical outcomes would depend on whether the modeled fees, fills, funding, adverse selection, and hedging frictions match actual venues.
Key ideas
- The market maker jointly controls bid-ask spreads and inventory hedging across exchanges.
- Profit and loss is decomposed into spread income, adverse selection, inventory cost, hedging friction, and funding exposure.
- The control problem is formulated with a Hamilton–Jacobi–Bellman equation under CARA utility.
- The framework analyzes profitable regimes, hedge choices, leverage limits, drawdown bounds, and portfolio allocation.
- Numerical figures illustrate shifts between profitable and unprofitable regions, while live performance is not established in the abstract.
Tags
Full text
# 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.
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