2025/05/08 by Alex Nezlobin, Nezlobin, Alex, Martin Tassy +1 · 3 citations
Business, Management and Accounting · Computer Science · Economics, Econometrics and Finance · #Banking stability, regulation, efficiency #Blockchain Technology Applications and Security #Digital Platforms and Economics #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.2505.05113
openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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: ARB= \frac σb2 2+√(2π) γ/(|ζ(1/2)| σb) +O (e^-const\tfracγσb) ≈ \fracσb2 2 + 1.7164 γ/σb, where σb 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.