Multi-Currency AMMs for Decentralized FOREX Markets: Feasibility & Optimal Design
arXiv:2607.26405
The paper proposes a multi‑currency automated market maker design for decentralized foreign‑exchange markets that shares liquidity across many currency pairs, derives optimal pool weights to minimize trading costs, and uses hierarchical clustering to group currencies into efficient pools, showing about a 13% cost reduction versus traditional vehicle‑currency routing.
Abstract
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.