A Microstructure Analysis of Coupling in CFMMs

Battle Count: 62

Highly relevant for DeFi quantitative trading and market making. The paper provides exact closed-form expressions for slippage, price drift transmission, and marginal cost in coupled AMM routes, which are directly applicable to execution algorithms, liquidity provision strategies, and risk management in DeFi. The compound curvature analysis informs optimal liquidity placement across chained pools. The oracle market framework is relevant for understanding price discovery in long-tail token markets. However, the paper is purely analytical with no empirical backtesting or live trading results, and does not address MEV, gas costs, or other practical execution considerations.

The mathematical derivations are moderately complex, involving multivariable calculus, Taylor expansions, and convex optimization concepts. However, the final closed-form expressions for the CPMM case are tractable and directly implementable. The general CFMM framework requires specifying an invariant function and computing its derivatives. Numerical evaluation of the marginal cost and depth functions is straightforward given the derived swap, drift, and depth formulas. The main complexity lies in understanding the coupled state-space model and the perturbation expansion, not in the final computational implementation.

The paper provides fully self-contained mathematical derivations with explicit closed-form expressions for the CPMM case study. All case-study parameters (reserves x=10^7, y1=4.5x10^8, y2=7.2x10^7, z=10^9, fee=3%) are specified. Supplementary materials are referenced for explicit CPMM marginal cost functions. However, no code repository or numerical implementation is provided, and the general CFMM results require a specific invariant function to evaluate. The analytical framework is reproducible from the equations given, but empirical validation against real market data is absent.