level: research
a new paper presents a mathematical framework for market making in perpetual futures markets where maker fees are zero. the problem is set up as a stochastic optimal control task on a filtered probability space. the market maker adjusts bid-ask spreads and hedges inventory across two exchanges. the work breaks down profit and loss into five parts: spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure.
the authors derive a hamilton-jacobi-bellman equation for the joint control problem under constant absolute risk aversion utility. they provide a verification theorem to confirm the solution. a key result is a set of high-apy regime theorems that identify profitable conditions using five dimensionless parameters. these lead to a master apy formula that quantifies expected returns. the analysis also covers zero-fee economics on decentralized exchanges, giving optimal entry and exit thresholds for market makers.
the framework addresses cross-exchange hedging, where a market maker can offset risk by trading on a second venue. this helps manage inventory imbalances and reduce exposure to adverse price moves. the theoretical results aim to guide automated market making strategies in crypto derivatives. the paper focuses on perpetual futures, a popular instrument in decentralized finance, and shows how zero maker fees change the optimal behavior compared to traditional markets.
why it matters: it provides a rigorous basis for designing automated market making algorithms in crypto derivatives, potentially improving liquidity and profitability on decentralized exchanges.