Table of Links 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 Graphs and Tables 5 Model The major metric to consider for evaluation of the cross-border CBDCs exchange is the cost of the CBDCs swap. In general, the total cost of DeFi service consists of three components: [31], [19] TotalCost = GasFee + DeFiExplicitFee + DeFiImplicitFee Gas Fees are paid to the blockchain operators for executing the transaction. In the case of transactions on roll-ups, the gas fee is comprised of both the L1 and L2 gas fee components. DeFi Explicit Fee is charged by the DeFi protocol for the provided service. In the case of token swap at AMM-DEX, the liquidity pool fee (LP Fee) is the explicit fee charged by the DEX, and part of it (or whole) is distributed to the liquidity providers (LPs) to the pool. DeFi Implicit Fee are indirect fees specific to the design of the DeFi protocol. Price impact and slippage are implicit fees accrued by a trader when swapping tokens at AMM [31], [19] and refer to the difference between quoted and executed price by the AMM. Price impact is caused by the transaction volume and slippage (positive or negative) results from other swaps occurring within the same block as the transaction swap. Further the following model for the total cost of swap is considered: TotalSwapCost = GasFee + LPFee + PriceImpact LP Fee is typically the percentage of the transaction volume, and liquidity providers supply capital to the AMM’s liquidity pools in exchange for participation in LP fees. Price impact is the change in exchange price caused by the transaction volume and is specific to the AMM type and the liquidity pool size. The next section presents the major AMM types and corresponding price impact calculation methods. 5.1 Automated Market Makers Constant Product with Concentrated Liquidity Market Maker (CLMM) - Uniswap v3 Stableswap Invariant - Curve v1 Cryptoswap Invariant - Curve v2 As in equation (4), but with K defined as 5.2 Price Impact 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. 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 5 Model The major metric to consider for evaluation of the cross-border CBDCs exchange is the cost of the CBDCs swap. In general, the total cost of DeFi service consists of three components: [31], [19] TotalCost = GasFee + DeFiExplicitFee + DeFiImplicitFee TotalCost = GasFee + DeFiExplicitFee + DeFiImplicitFee Gas Fees are paid to the blockchain operators for executing the transaction. In the case of transactions on roll-ups, the gas fee is comprised of both the L1 and L2 gas fee components. Gas Fees DeFi Explicit Fee is charged by the DeFi protocol for the provided service. In the case of token swap at AMM-DEX, the liquidity pool fee (LP Fee) is the explicit fee charged by the DEX, and part of it (or whole) is distributed to the liquidity providers (LPs) to the pool. DeFi Explicit Fee DeFi Implicit Fee are indirect fees specific to the design of the DeFi protocol. Price impact and slippage are implicit fees accrued by a trader when swapping tokens at AMM [31], [19] and refer to the difference between quoted and executed price by the AMM. Price impact is caused by the transaction volume and slippage (positive or negative) results from other swaps occurring within the same block as the transaction swap. DeFi Implicit Fee Further the following model for the total cost of swap is considered: TotalSwapCost = GasFee + LPFee + PriceImpact TotalSwapCost = GasFee + LPFee + PriceImpact LP Fee is typically the percentage of the transaction volume, and liquidity providers supply capital to the AMM’s liquidity pools in exchange for participation in LP fees. Price impact is the change in exchange price caused by the transaction volume and is specific to the AMM type and the liquidity pool size. The next section presents the major AMM types and corresponding price impact calculation methods. 5.1 Automated Market Makers Constant Product with Concentrated Liquidity Market Maker (CLMM) - Uniswap v3 Constant Product with Concentrated Liquidity Market Maker (CLMM) - Uniswap v3 Stableswap Invariant - Curve v1 Stableswap Invariant - Curve v1 Cryptoswap Invariant - Curve v2 As in equation (4), but with K defined as Cryptoswap Invariant - Curve v2 5.2 Price Impact 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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