Optimal Control of the Ethena Yield-Bearing Stablecoin

Battle Count: 83

Highly relevant to quantitative trading in crypto/DeFi markets. The paper provides explicit optimal execution strategies for delta-neutral carry trades involving perpetual futures, directly applicable to funding rate arbitrage, basis trading, and stablecoin yield optimization. The permanent/temporary price impact framework is directly transferable to algorithmic execution in crypto markets. The linear feedback control structure is implementable in real-time trading systems. The finite-horizon liquidation urgency model is relevant for any strategy with forced position closure deadlines.

The analytical solution is fully explicit, making implementation straightforward once parameters are estimated. The infinite-horizon case requires solving a scalar fixed-point equation (iterative) and evaluating closed-form expressions. The finite-horizon case requires numerically solving a backward system of 3 coupled Riccati ODEs plus 2 linear ODEs plus 1 quadrature. The main practical challenge is estimating the permanent impact coefficients (mu1, mu2) and temporary impact coefficients (lambda1, lambda2) from market microstructure data, as well as calibrating the OU basis dynamics. The Mathematica code provided demonstrates feasibility.

The paper provides complete analytical solutions with explicit formulas for all coefficients. Appendix A contains full Wolfram Mathematica code for reproducing all numerical experiments and plots (Figures 1 and 2). Parameter values are fully specified. The only limitation is that the code is in Mathematica rather than Python, and no external data is required (pure simulation).