Bounding LVR in AMMs via Secant-Tangent Divergence and Collateralized Liquidity Scaling

Hyoungsung Kim; Yong-Suk Park

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arXiv · 2605.19267

Bounding LVR in AMMs via Secant-Tangent Divergence and Collateralized Liquidity Scaling

Hyoungsung Kim·Yong-Suk Park

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Abstract

Automated Market Makers face a geometric dilemma: expanding liquidity depth to reduce execution slippage increases Liquidity Providers' exposure to toxic arbitrage, quantified as Loss-Versus-Rebalancing (LVR). We study the Hybrid Liquidity-Collateral Pool (HLCP), a stylized architecture that aims to partially decouple execution quality from active risk exposure through an N-scaled virtual invariant and a collateral buffer. The analysis first characterizes the geometric divergence between execution slippage and marginal-price deviation, then uses this divergence to motivate a trigger-based collateral injection rule. In a stylized duopoly model, under hyper-saturated background liquidity and non-zero volatility or collateral yield, adopting the HLCP is a Nash equilibrium and Pareto-improving relative to a standard AMM benchmark. Empirically, we examine two settings. Under a stochastic-volatility-with-jumps stress scenario, the trigger policy avoids one-shot total buffer depletion under the imposed control law and simulated shock path. Using 2025 Uniswap V2 data with zero collateral yield, the HLCP exhibits lower realized LVR and higher net LP return than the standard CPMM benchmark in the sample considered.

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Hyoungsung Kim, Yong-Suk Park. 2026-05-19. Bounding LVR in AMMs via Secant-Tangent Divergence and Collateralized Liquidity Scaling. https://arxiv.org/abs/2605.19267

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