Market Making for Perpetuals with Stochastic Funding Costs

Summary

This paper extends optimal market making to perpetual contracts where funding rates evolve stochastically. Because a market maker’s inventory affects both price exposure and funding cash flows, the authors formulate a joint inventory and funding control problem. They solve it with a monotone finite-difference method for the Hamilton-Jacobi-Bellman equation, then derive bid and ask quote offsets from changes in value across inventory levels.

Funding behavior is calibrated using Hyperliquid ETH, BTC, and SOL perpetual data. The authors use Gaussian Ornstein-Uhlenbeck funding as a tractable baseline and examine jump diagnostics that indicate heavy-tailed funding innovations. In holdout simulations with two fill-proxy calibrations, their method improves mean performance and reduces inventory RMS for ETH and BTC relative to classical Avellaneda-Stoikov. SOL shows positive gains against unscaled Avellaneda-Stoikov, but not a Pareto improvement against a risk-scaled diagnostic. The findings depend on simulation assumptions and proxy fills; the excerpt does not establish live-market results, and the jump behavior remains a future model extension.

Key ideas

• Perpetual market-making inventory affects both mark-to-market risk and funding cash flows.
• The control problem models inventory jointly with a stochastic funding state.
• A finite-difference HJB solution is used to derive bid and ask quote offsets.
• Gaussian Ornstein-Uhlenbeck funding serves as a tractable baseline despite evidence of heavy-tailed innovations.
• Holdout simulation results vary by asset and benchmark, with SOL lacking a Pareto improvement against risk-scaled Avellaneda-Stoikov.

Tags

# Funding-Aware Optimal Market Making for Perpetual DEXs


# Funding-Aware Optimal Market Making for Perpetual DEXs









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.