Optimal Control of the Ethena Yield-Bearing Stablecoin

TL;DR

This paper models and solves stochastic control problems for the Ethena DeFi stablecoin, optimizing yield strategies involving staking rewards and funding payments while accounting for price impacts.

Contribution

It provides explicit solutions for optimal control strategies in a DeFi stablecoin yield-generating protocol considering price impacts.

Findings

Explicit optimal control strategies derived for both infinite and finite horizon problems.

Model captures permanent and temporary price impacts affecting yield and funding income.

Strategies maximize protocol wealth considering liquidation costs and price impacts.

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.