Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Background
2.1 Layer-2 Blockchains
2.2 Project Mariana


Related Work and Contribution


System Architecture


Model
5.1 Automated Market Makers
5.2 Price Impact


Simulation
6.1 Data and Parameters
6.2 Results


Discussion


Conclusions, Acknowledgements, and References Background
2.1 Layer-2 Blockchains
2.2 Project Mariana Background 2.1 Layer-2 Blockchains 2.1 Layer-2 Blockchains 2.2 Project Mariana 2.2 Project Mariana Related Work and Contribution Related Work and Contribution Related Work and Contribution System Architecture System Architecture System Architecture Model
5.1 Automated Market Makers
5.2 Price Impact Model Model 5.1 Automated Market Makers 5.1 Automated Market Makers 5.2 Price Impact 5.2 Price Impact Simulation
6.1 Data and Parameters
6.2 Results Simulation 6.1 Data and Parameters 6.1 Data and Parameters 6.2 Results 6.2 Results Discussion Discussion Discussion Conclusions, Acknowledgements, and References Conclusions, Acknowledgements, and References Conclusions, Acknowledgements, and References Graphs and Tables Graphs and Tables 3 Related Work and Contribution There is an abundance of literature discussing the implementation of CBDCs in various countries [23], [13], [12], [21], [5], but little research on the exchange between CBDCs in AMMs, except for Project Mariana [4]. Lipton and Sepp[20] study the implicit costs (price impact) for G-10 CBDCs exchange at AMM with Concentrated Liquidity (Uniswap v3). This work is the first research that takes the holistic approach to analyze the total costs of CBDCs exchange at various AMMs, including Stableswap Invariant (Curve v2), applied in Project Mariana. This study found that a multi-AMM set-up for CBDCs exchange on L2 is more cost-efficient than a single AMM of Project Mariana, despite the fragmentation of liquidity among various AMMs. Such a multi-AMM system on private L2 is further presented, and its behavior is evaluated via simulation based on the historical FX rates, Mariana Project set up as a benchmark. This work makes the following contributions. – Demonstrating that multi-AMMs set-up for CBDCs exchange is more costefficient than a single AMM. – Designing such multi-AMMs set-up for CBDCs exchange using L2 and L3 blockchains and demonstrating its superior performance for small, medium, and largest transaction volumes and any transaction in case of spikes of gas fees. – Conducting first detailed analysis of the total costs of CBDCs swaps on AMM-DEX—gas fees, swap fees (explicit fees), and price impact (explicit fees), among various AMMs and L1 and L2-based DEXes. – Providing quantitative metrics to evaluate the efficiency of cross-border CBDCs on DEXes for major AMMs. Their implementation is available in the public GitHub repository [17] – Building a framework for simulation based on historical FX rate that can be replicated in other cross-border CBDCs projects or in permission DeFi in the Ethereum ecosystem. For all metrics, the mathematical background and numerical methods with the implementation are provided, such as the Newthon-Raphon method for price impact in Cryptoswap Invariant AMM applied in Project Mariana. Authors:
(1) Krzysztof Gogol, University of Zurich (gogol@ifi.uzh.ch);
(2) Johnnatan Messias, Matter Labs;
(3) Malte Schlosser, University of Zurich;
(4) Benjamin Kraner, University of Zurich;
(5) Claudio Tessone, University of Zurich. Authors: Authors: (1) Krzysztof Gogol, University of Zurich (gogol@ifi.uzh.ch); (2) Johnnatan Messias, Matter Labs; (3) Malte Schlosser, University of Zurich; (4) Benjamin Kraner, University of Zurich; (5) Claudio Tessone, University of Zurich. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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