Loss-Versus-Rebalancing under Deterministic and Generalized block-times
Loss-Versus-Rebalancing under Deterministic and Generalized block-times ArXiv ID: 2505.05113 “View on arXiv” Authors: Alex Nezlobin, Martin Tassy Abstract Although modern blockchains almost universally produce blocks at fixed intervals, existing models still lack an analytical formula for the loss-versus-rebalancing (LVR) incurred by Automated Market Makers (AMMs) liquidity providers in this setting. Leveraging tools from random walk theory, we derive the following closed-form approximation for the per block per unit of liquidity expected LVR under constant block time: [" \overline{"\mathrm{ARB"}}= \frac{",σ_b^{2"}} {",2+\sqrt{2π"},γ/(|ζ(1/2)|,σ_b),}+O!\bigl(e^{"-\mathrm{const"}\tfracγ{“σ_b”}}\bigr);\approx; \frac{“σ_b^{2”}}{",2 + 1.7164,γ/σ_b"}, "] where $σ_b$ is the intra-block asset volatility, $γ$ the AMM spread and $ζ$ the Riemann Zeta function. Our large Monte Carlo simulations show that this formula is in fact quasi-exact across practical parameter ranges. Extending our analysis to arbitrary block-time distributions as well, we demonstrate both that–under every admissible inter-block law–the probability that a block carries an arbitrage trade converges to a universal limit, and that only constant block spacing attains the asymptotically minimal LVR. This shows that constant block intervals provide the best possible protection against arbitrage for liquidity providers. ...