The Price of Liquidity: Implied Volatility of Automated Market Maker Fees

Battle Count: 95

Highly relevant for DeFi quantitative trading and market making. The paper provides a novel framework for quoting implied volatilities and correlations from AMM fee data, which could be used for options pricing, risk management, and hedging strategies in decentralized exchanges. The fixed-for-floating swap concept is directly applicable to liquidity provider hedging. However, the practical implementation is still theoretical (no on-chain swap exists yet), limiting immediate applicability.

The theoretical framework involves advanced stochastic calculus (Itô's lemma, martingale theory, optimal stopping), convex analysis for AMM characterization, and batch auction mechanism design. The closed-form solutions for CPMM implied volatility and correlation are elegant but the general AMM case requires numerical methods (Monte Carlo simulation, bisection search as noted for Curve v1). Implementing the proposed swap as a smart contract adds significant engineering complexity.

The paper provides detailed mathematical derivations, explicit formulas for implied volatility and correlation, and specifies exact smart contract addresses (e.g., 0x88e6a0c2ddd26feeb64f039a2c41296fcb3f5640 for WETH/USDC Uniswap v3 pool). However, the simulated CPMM/Curve data generation code and specific data processing pipelines are not publicly available. The theoretical framework is fully reproducible given the mathematical proofs in Appendix A.