Optimal Control of the Ethena Yield-Bearing Stablecoin

2026-05-11

AI Summary

This study addresses the optimal execution problem of simultaneously establishing long positions in stETH and short positions in ETH perpetual futures within the Ethena protocol, explicitly accounting for both permanent and temporary price impacts to maximize protocol returns. A continuous-time stochastic control framework is developed to model the joint dynamics of staking yields and funding rates under a delta-neutral strategy, marking the first integration of these two forms of price impact into a DeFi yield optimization setting. Explicit optimal trading rates are derived under both an infinite-horizon discounted formulation and a finite-horizon setup incorporating liquidation penalties, yielding implementable dynamic rebalancing rules for the protocol.

Abstract

We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with an equal-sized short position in ETH perpetual futures. The combined position is delta-neutral with respect to the ETH spot price, yet earns carry from two sources: staking rewards on the stETH leg, and funding-rate payments received from long perpetual holders when the perpetual trades at a premium to spot. A key feature of our model is that the control -- the rate of simultaneously buying stETH and shorting the perpetual -- exerts two distinct types of price impact. \textit{Permanent} impact shifts the mid-market prices of both legs, compressing the basis and permanently eroding future funding income. \textit{Temporary} impact reflects execution slippage on each leg. We study both an infinite-horizon discounted problem and a finite-horizon problem in which the protocol maximizes total wealth up to a fixed date $T$, subject to a terminal cost for liquidating any remaining position. In both cases the optimal control is obtained explicitly.

Problem

• optimal control
• stablecoin
• delta-neutral
• price impact
• DeFi

Innovation

• stochastic control
• delta-neutral strategy
• price impact
• DeFi stablecoin
• funding rate