SPIDE modeling paper on Uniswap V3 concentrated liquidity dynamics released
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Cheuk Yin Lee, Jimmy Risk, Shen-Ning Tung, and Tai-Ho Wang have released a paper on dynamic modeling of liquidity distributions for Uniswap V3 and other concentrated liquidity automated market makers based on stochastic partial integro-differential equations (SPIDEs). This study proves the existence and uniqueness of mild solutions in weighted L² spaces, and simplifies the SPIDE into a system of coupled linear stochastic differential equations, enabling the derivation of tractable expressions for pool reserves, pool value, and rebalancing losses. Finite-rank calibration on three Uniswap pools shows that, in two pools consistent with stationary settings, active range prediction errors are lower than the martingale benchmark.
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- arXiv q-finDynamics of Liquidity Distribution in Concentrated Liquidity Provision: A SPIDE Approach
Researchers use stochastic partial integro-differential equations (SPIDE) to model the dynamics of liquidity distribution in Uniswap V3 and other concentrated liquidity automated market makers. They prove the existence and uniqueness of mild solutions in a weighted L² space and reduce the SPIDE to a coupled system of linear stochastic differential equations. The model yields tractable expressions for pool reserves, pool value, and rebalancing losses. Finite-rank calibration on three Uniswap pools shows that, in two pools consistent with a stationary setting, prediction errors for active ranges are lower than a martingale benchmark.
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