Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices
Abstract
Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time Δt → 0; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LVR rate splits into a diffusion channel carrying the known multiplier F(γ/(σ√(Δt))) and a jump channel λV · G(γ;m,δ2) carrying no Δt, the two interacting only through an explicitly bounded remainder. The block schedule therefore governs only one channel. For symmetric jump laws the jump channel is moreover an exact lower bound, ℓ(Δt) ≥ λV G > 0, so the rate does not vanish as Δt → 0, and descends slowly, as √(Δt). At Ethereum's calibrated 12-second slot the rate is 471 bp/yr against a floor of 125, so only three quarters of LP loss is schedule-addressable. At Solana's 400 ms slot the jump channel already dominates. Netting the rate against per-block consensus cost, the LP-side optimal block time is invariant in pool size and in every jump parameter (λ,m,δ): jumps shift the level of LP loss but not the planner's marginal tradeoff. Volatility, the fee tier, and consensus cost set the optimum, near 8 s. However, LVR is only one input to block-time welfare, so this bounds the LP-side contribution rather than settling the design question.
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BibTeX
@misc{bundi2026optimal,
title = {{Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices}},
author = {Nils Bundi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30321},
eprint = {2608.30321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30321},
}
RIS
TY - UNPB
TI - Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices
AU - Nils Bundi
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30321
UR - https://arxiv.org/abs/2608.30321
AB - Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time Δt → 0; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LVR rate splits into a diffusion channel carrying the known multiplier F(γ/(σ√(Δt))) and a jump channel λV · G(γ;m,δ^2) carrying no Δt, the two interacting only through an explicitly bounded remainder. The block schedule therefore governs only one channel. For symmetric jump laws the jump channel is moreover an exact lower bound, ℓ(Δt) ≥ λV G > 0, so the rate does not vanish as Δt → 0, and descends slowly, as √(Δt). At Ethereum's calibrated 12-second slot the rate is 471 bp/yr against a floor of 125, so only three quarters of LP loss is schedule-addressable. At Solana's 400 ms slot the jump channel already dominates. Netting the rate against per-block consensus cost, the LP-side optimal block time is invariant in pool size and in every jump parameter (λ,m,δ): jumps shift the level of LP loss but not the planner's marginal tradeoff. Volatility, the fee tier, and consensus cost set the optimum, near 8 s. However, LVR is only one input to block-time welfare, so this bounds the LP-side contribution rather than settling the design question.
ER -