跳扩散价格下自动做市商流动性提供者的最优出块时间
Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices
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中文总结 AI 辅助
本文针对跳扩散价格下的AMM流动性提供者，将LVR速率分解为扩散与跳变渠道，推导得出最优出块时间约为8秒，且与池规模、跳变参数无关。
中文摘要 AI 辅助
损失与再平衡（LVR）是自动做市商（AMM）上流动性提供者（LP）承担的主要逆向选择成本。在几何布朗运动假设下，套利利润与盈利区块的概率成正比，当区块时间Δt趋近于0时，该概率趋近于0，这是支持不断缩短区块时间的现有论点。本文将参考价格建模为跳扩散过程，证明常数乘积型AMM的LVR速率可分解为两个渠道：扩散渠道，其带有已知乘数F(γ/(σ√Δt))；跳变渠道，其带有λV·G(γ;m,δ²)且不含Δt，两者仅通过显式有界的余项相互作用。因此，区块调度仅对其中一个渠道产生影响。对于对称跳变定律，跳变渠道同时是精确下界，即ℓ(Δt)≥λVG>0，故当Δt趋近于0时，LVR速率不会消失，而是以√Δt的速度缓慢下降。在以太坊校准的12秒出块间隔下，LVR速率为每年471个基点，而其下界为125个基点，因此仅四分之三的LP损失可通过区块调度解决；在Solana的400毫秒出块间隔下，跳变渠道已占据主导地位。将该速率与每区块共识成本相抵后，LP侧的最优出块时间在池规模以及所有跳变参数（λ,m,δ）下保持不变：跳变会改变LP损失的水平，但不会影响设计者的边际权衡。最优出块时间由波动率、费率层级和共识成本决定，约为8秒。不过，LVR仅为区块时间福利的一个输入因素，因此本文的结论仅限定于LP侧的贡献，并未解决区块时间设计的整体问题。
英文摘要
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.
发表机构
- Zurich University of Applied Sciences（苏黎世应用科技大学）
机构由 AI 辅助整理，请以论文原文为准。
