Optimal Control of the Ethena Yield-Bearing Stablecoin

Paper: arXiv 2605.11263

Authors: Matthew Lorig

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical formulation using stochastic control to address the novel problem of optimizing Ethena’s delta-neutral yield strategy under market impact constraints. While the theoretical derivations and explicit solutions are high quality, the work lacks empirical backtesting and real-world dataset validation.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Optimize Ethena Yield Strategy via Stochastic Control"] --> B["Inputs & Strategy:<br>Delta-Neutral stETH Long + ETH Perps Short,<br>Staking Yield, Funding Rates, Dual Price Impact"]
    B --> C["Formulate Stochastic Control Models:<br>Infinite-Horizon & Finite-Horizon with Terminal Cost"]
    C --> D["Account for Price Impact:<br>Permanent Basis Shift & Temporary Slippage"]
    D --> E["Derive Explicit Optimal Control Policy"]
    E --> F["Key Outcome:<br>Explicit Optimal Execution Rate for Maximum Protocol Wealth"]

Cited References (35)

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2. What explains the stock market’s reaction to F ederal R eserve policy? (2005)
3. Risk, uncertainty and monetary policy (2013)
4. Are simple technical trading rules profitable in bitcoin markets? (2024)
5. Market Volatility, Monetary Policy, and the Term Premium (2017) — link
6. What Explains the Stock Market’s Reaction to F ederal R eserve Policy? (2005) — link
7. Risk, Uncertainty and Monetary Policy (2013) — link
8. Monetary Policy and the VIX (2008)

1 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.