Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices

Battle Count: 69

Highly relevant for DeFi market-making strategies, LP position management, and understanding the economic limits of block-time optimization. Directly informs fee-tier design, arbitrage timing, and the cost-benefit analysis of protocol upgrades (e.g., Ethereum's block-time changes). The jump floor concept is critical for realistic LP loss estimation in crypto markets where price discontinuities are pervasive.

The analytical framework is mathematically sophisticated (Itô-Lévy calculus, integro-differential equations, Cardano's formula for cubic roots) but yields closed-form solutions. Practical implementation requires: (1) jump-diffusion calibration from tick/minute data (bipower variation, Lee-Mykland test), (2) evaluation of F(κ) and G(γ;m,δ²) functions, (3) solving the cubic for optimal Δt. The numerical quadrature for the exact rate (6) and the mixing condition verification add moderate complexity.

The paper provides fully closed-form analytical results (Theorems 1-4, Lemmas 1-2, Proposition 1), explicit calibration parameters (Table 1), and a clear data pipeline (Binance ETH/USDT 5-min closes, bipower variation, Lee-Mykland jump test). All proofs are included in the appendix. The main reproducibility gap is the absence of a public code repository, though all formulas are analytically tractable.