Paper: Multi-Currency AMMs for Decentralized FOREX Markets: Feasibility & Optimal Design
Authors: Reina Ke Xin Li, Andreas Park, Andreas Veneris, Srisht Fateh Singh
Date: 2026-07-29
Estimated Reading Time: 31 minutes
This paper studies whether multi-currency automated market makers (AMMs) can reduce foreign exchange trading costs compared with the conventional model of routing trades through a vehicle currency such as the US dollar. The authors develop a theoretical framework based on constant-mean AMMs that jointly models price impact, liquidity provision, trading fees, and impermanent loss. The framework derives equilibrium trading costs as functions of exchange rate volatility, trading volume, and pool composition, and produces analytical results for optimal asset weights under several market structures. For more general settings, the paper proposes an approximation for weight optimization and formulates the broader problem of assigning currencies into multi-currency pools. A hierarchical agglomerative clustering algorithm is introduced to construct currency pools using exchange rate correlations and bilateral trade data. Empirical evaluation using data for 43 non-pegged currencies from 2008 to 2023 finds that the proposed architecture reduces realized aggregate trading costs by approximately 13% relative to bilateral USD routing while maintaining similar performance during periods of financial stress.
Core insights
- Optimal trading costs depend on multiple variables. Equilibrium trading costs are determined jointly by trading volume, exchange rate volatility, pool composition, and liquidity provider incentives. The framework explicitly models the interaction between price impact and impermanent loss when selecting AMM parameters.
- Pool weights should reflect risk and activity. Equal weighting is generally not cost minimizing. The optimal allocation assigns lower exposure to currencies that contribute relatively high impermanent loss while assigning greater weight to currencies associated with stronger trading demand.
- Liquidity consolidation creates measurable trade-offs. Combining many currencies into a shared liquidity pool reduces price impact through deeper aggregate liquidity. The resulting increase in impermanent loss must be offset through careful weight optimization and fee selection.
- Currency selection is as important as weight selection. The paper formulates currency grouping as an optimization problem and proposes hierarchical agglomerative clustering based on exchange rate correlations. The resulting pools naturally group currencies with similar economic and regional characteristics because such currencies exhibit lower relative volatility.
- Empirical evidence supports the proposed architecture. Using historical exchange rate and international trade data, the optimized pool structure reduced realized aggregate trading costs by about 13% compared with vehicle-currency routing. The reported savings remained relatively stable during the 2008 financial crisis and the 2020 COVID-19 period.
The paper develops a market design framework rather than introducing a blockchain token or governance token. Consequently, the economic analysis centers on liquidity provision instead of token issuance, emissions, or staking incentives. The principal economic variables are trading fees, liquidity depth, exchange rate volatility, and currency weights within the AMM. Supply is represented by liquidity providers supplying currency reserves, while demand is represented by foreign exchange trading volume. How sensitive would the proposed equilibrium remain if liquidity providers required compensation for risks beyond impermanent loss, such as smart contract or settlement risks?
The proposed equilibrium links liquidity provider incentives directly to trading costs. Liquidity providers participate until expected fee income equals expected impermanent loss, after which equilibrium liquidity depth determines price impact. Rewards therefore arise entirely from trading fees rather than token emissions or protocol subsidies. This framework avoids relying on external incentive mechanisms and instead derives compensation from market activity itself. The optimization problem balances two opposing effects. Larger consolidated pools reduce price impact because more liquidity supports every trading pair, but adding currencies with high relative volatility increases impermanent loss. The proposed weighting mechanism shifts exposure toward currencies with stronger trading activity and lower volatility contribution. Would the same optimization remain effective if exchange rate correlations changed rapidly across shorter time horizons than those used for calibration?
Beyond individual pool design, the paper extends optimization to the entire foreign exchange network. Rather than placing every currency into one pool, the authors partition currencies into multiple pools using hierarchical agglomerative clustering based on historical correlations. This produces economically interpretable groupings while reducing estimated aggregate trading costs. Demand concentration is therefore managed through pool assignment instead of relying solely on a single global liquidity pool.
The empirical analysis provides evidence that optimized pool composition can outperform bilateral vehicle-currency routing under the assumptions of the proposed framework. The reported reduction of approximately 13% in realized aggregate trading costs results from jointly optimizing weights, fees, and pool membership using historical exchange rate and trade data. The paper also acknowledges assumptions that may influence these results, including fixed pool membership during evaluation, simplified liquidity provider behavior, and historical estimation of future volatility and trading volume. Future work suggested by the authors includes dynamic pool rebalancing, richer market dynamics, alternative partitioning algorithms, and analytical solutions for the general optimization problem.
