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

Source 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 $Δt \to 0$; 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 $F(γ/(σ\sqrt{Δt}))$ and a jump channel $λV \cdot G(γ;m,δ^2)$ 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, $\ell(Δt) \ge λV G > 0$, so the rate does not vanish as $Δt \to 0$, and descends slowly, as $\sqrt{Δt}$. 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.