Optimal Trading Control for an ETH Yield-Bearing Stablecoin

Summary

The paper models the yield strategy of a decentralized stablecoin that combines staked Ethereum with an equal-sized short position in ETH perpetual futures. The matched legs aim to reduce exposure to ETH spot-price changes while earning staking rewards and, when perpetual funding is positive, payments from perpetual holders. The strategy’s returns therefore depend on both staking income and the funding environment.

The authors formulate stochastic control problems in which the protocol chooses how quickly to build the paired position. Trading affects prices in two ways: permanent impact compresses the basis and reduces future funding income, while temporary impact creates execution slippage. They derive explicit optimal controls for both an infinite-horizon discounted objective and a finite-horizon wealth objective that includes a cost for liquidating residual holdings. The results are model-based; the description does not provide empirical validation or details on how sensitive the controls are to assumptions about funding, impact, or liquidation costs.

Key ideas

• The modeled strategy pairs staked ETH with an equal-sized short in ETH perpetual futures.
• The paired exposure aims to offset ETH spot moves while collecting staking rewards and potentially positive funding.
• Permanent price impact can compress the basis and reduce future funding income.
• Temporary price impact represents execution slippage on the two legs.
• The paper derives optimal controls for both infinite and finite investment horizons.

Tags

# Optimal Control of the Ethena Yield-Bearing Stablecoin


# Optimal Control of the Ethena Yield-Bearing Stablecoin









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.

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.