AI 中文总结
本文针对去中心化外汇市场，提出多货币AMM池设计，结合层次凝聚聚类算法划分货币，实证显示较载体货币路由降低约13%交易成本，在金融压力期收益稳定。
AI 中文摘要
大多数货币对缺乏直接的流动性市场，因此国际外汇交易依赖于通过主导载体货币进行交易路由。多货币自动做市商（AMM）通过在众多货币对之间共享流动性提供了一种替代方案，在利用流动性整合的同时促进直接跨境货币交易。本文研究了一种可最小化交易成本的多货币池设计。在常均值AMM架构下，均衡交易成本反映了整合流动性带来的价格影响降低与联合回报风险导致的无常损失增加之间的权衡。本研究推导了闭式成本表达式，确定了最优池权重，并表明在一系列市场参数范围内，优化后的多货币池优于现状方案。随后，本文构建了将货币划分为多货币池的系统级问题，并使用层次凝聚聚类算法求解。基于2008年至2023年间43种货币的汇率及交易数据进行实证分析，该算法运行时间为1.6秒，生成的池具有地理和经济结构。值得注意的是，与载体货币路由的现状相比，这一方案将实现的成本降低了约13%，且在全球金融压力时期收益稳定。
英文摘要
Most currency pairs lack a direct liquid market, so international foreign exchange relies on routing transactions through a dominant vehicle currency. Multi-currency automated market makers (AMMs) offer an alternative by sharing liquidity across many currency pairs, facilitating direct cross-currency trade while exploiting liquidity consolidation. This paper studies a multi-currency pool design that minimizes trading cost. Under a constant-mean AMM architecture, equilibrium trading costs reflect the trade-off between reduced price impact from consolidated liquidity and increased impermanent loss from joint return risk. This work derives closed-form costs, characterizes optimal pool weights, and shows that the optimized multi-currency pool dominates the status quo over a range of market parameters. It then formulates the system-level problem of partitioning currencies into multi-currency pools, which is solved using a hierarchical agglomerative clustering algorithm. Empirically, using exchange rate and trade data for 43 currencies over 2008-2023, the algorithm runs in 1.6 seconds and produces pools with geographic and economic structure. Notably, this reduces realized costs by ~13% relative to the status quo of vehicle-currency routing, with gains stable through episodes of global financial stress.
