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Cross-border Exchange of CBDCs using Layer-2 Blockchain

Krzysztof Gogol, Johnnatan Messias, Malte Schlosser, Benjamin Kraner, Claudio Tessone

TL;DR

The paper tackles the high costs and liquidity fragmentation in cross-border CBDC exchanges by proposing a multi-layer architecture: a private L2 rollup on a public L1, augmented with multiple L3 AMMs and a Rule-based router to dynamically select the cheapest path. It introduces a formal cost model decomposing total swap cost into $Total\ Swap\ Cost = Gas\ Fee + LP\ Fee + PriceImpact$, and evaluates competing AMMs (CFMMs, CLMMs, and Curve v2) under a three-CBDC pool (CHF, EUR, SGD) using historical FX data. Through FX-based back-testing, the study demonstrates that distributing liquidity across several L3 AMMs yields lower costs than a single L1 AMM (Project Mariana), with gas fees and price impact behaving differently across small, medium, and large trades. The findings support a scalable, privacy-preserving, and cost-efficient cross-border CBDC marketplace, highlighting the practical advantages of L2/L3 orchestration for regulatory-compliant DeFi interactions. The work also provides a framework and public codebase to replicate the simulations and extend the analysis to other CBDC families.

Abstract

This paper proposes a novel multi-layer blockchain architecture for the cross-border trading of CBDCs. The permissioned layer-2, by relying on the public consensus of the underlying network, assures the security and integrity of the transactions and ensures interoperability with domestic CBDCs implementations. Multiple Layer-3s operate various Automated Market Makers (AMMs) and compete with each other for the lowest costs. To provide insights into the practical implications of the system, simulations of trading costs are conducted based on historical FX rates, with Project Mariana as a benchmark. The study shows that, even with liquidity fragmentation, a multi-layer and multi-AMM setup is more cost-efficient than a single AMM.

Cross-border Exchange of CBDCs using Layer-2 Blockchain

TL;DR

The paper tackles the high costs and liquidity fragmentation in cross-border CBDC exchanges by proposing a multi-layer architecture: a private L2 rollup on a public L1, augmented with multiple L3 AMMs and a Rule-based router to dynamically select the cheapest path. It introduces a formal cost model decomposing total swap cost into , and evaluates competing AMMs (CFMMs, CLMMs, and Curve v2) under a three-CBDC pool (CHF, EUR, SGD) using historical FX data. Through FX-based back-testing, the study demonstrates that distributing liquidity across several L3 AMMs yields lower costs than a single L1 AMM (Project Mariana), with gas fees and price impact behaving differently across small, medium, and large trades. The findings support a scalable, privacy-preserving, and cost-efficient cross-border CBDC marketplace, highlighting the practical advantages of L2/L3 orchestration for regulatory-compliant DeFi interactions. The work also provides a framework and public codebase to replicate the simulations and extend the analysis to other CBDC families.

Abstract

This paper proposes a novel multi-layer blockchain architecture for the cross-border trading of CBDCs. The permissioned layer-2, by relying on the public consensus of the underlying network, assures the security and integrity of the transactions and ensures interoperability with domestic CBDCs implementations. Multiple Layer-3s operate various Automated Market Makers (AMMs) and compete with each other for the lowest costs. To provide insights into the practical implications of the system, simulations of trading costs are conducted based on historical FX rates, with Project Mariana as a benchmark. The study shows that, even with liquidity fragmentation, a multi-layer and multi-AMM setup is more cost-efficient than a single AMM.
Paper Structure (14 sections, 8 equations, 9 figures, 1 table)

This paper contains 14 sections, 8 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Layer-2 Blockchains
  4. Project Mariana
  5. Related Work and Contribution
  6. System Architecture
  7. Model
  8. Automated Market Makers
  9. Price Impact
  10. Simulation
  11. Data and Parameters
  12. Results
  13. Discussion
  14. Conclusions

Figures (9)

  • Figure 1: Architecture of Rollup—Layer-2 blockchain that stores state in underlying Layer-1 blockchain
  • Figure 2: Project Mariana Architecture: Cross-Border CBDC Exchange using Cryptoswap Invariant AMM
  • Figure 3: General Architecture of Cross-Border CBDCs Exchange using L3 and L2 Blockchains on Public L1 Blockchain
  • Figure 4: Difference between the total swap costs at L1-Mariana and L2-L3-Exchange. The negative difference indicates L2-L3-Exchange out-performance for small and large transaction volumes.
  • Figure 5: Breakdown of total swap costs into gas fees, LP fees (swap fee) and price impact (slippage) as a function of the swap volume
  • ...and 4 more figures