Better market Maker Algorithm to Save Impermanent Loss with High Liquidity Retention

• Main Authors: Yan, CY, Keol, Steve, Co, Xo, Leung, Nate
• Format: Journal Article
• Language: English
• Published: 27.02.2025
• Subjects: Quantitative Finance - Trading and Microstructure
• DOI: 10.48550/arxiv.2502.20001

Decentralized exchanges (DEXs) face persistent challenges in liquidity retention and user engagement due to inefficiencies in conventional automated market maker (AMM) designs. This work proposes a dual-mechanism framework to address these limitations: a ``Better Market Maker (BMM)'', which is a liquidity-optimized AMM based on a power-law invariant ( $X^nY = K$ ,$n = 4$ ), and a dynamic rebate system (DRS) for redistributing transaction fees. The segment-specific BMM reduces impermanent loss by 36\% compared to traditional constant-product ( $XY = K$ ) models, while retaining 3.98x more liquidity during price volatility. The DRS allocates fees ( $\gamma V$ ,$\gamma \in \{0.003, 0.005, 0.01\}$ ) with a rebate ratio$\rho \in [0.3, 0.4]$to incentivize trader participation and maintain continuous capital injection. Simulations under high-volatility conditions demonstrate impermanent loss reductions of 36.0\% and 40\% higher user engagement compared to static fee models. By segmenting markets into high-, mid-, and low-volatility regimes, the framework achieves liquidity depth comparable to centralized exchanges (CEXs) while maintaining decentralized governance and retaining value within the cryptocurrency ecosystem.