Pricing and Hedging for Liquidity Provision in Constant Function Market Making

Battle Count: 60

Highly relevant for quantitative trading in DeFi and crypto markets. The framework provides actionable tools for: (1) pricing and hedging LP positions as derivatives, (2) computing Greeks (Delta, Gamma, Vega) for liquidity positions, (3) designing optimal bonding curves, (4) implementing delta-hedging strategies for IL, (5) extracting implied volatility from liquidity profiles for market-making decisions, and (6) determining optimal exit timing via last-passage analysis. Directly applicable to crypto options market-making, DeFi protocol design, and systematic liquidity provision strategies. The empirical validation with real Uniswap V3 and Deribit data enhances practical relevance.

The theoretical framework involves advanced mathematical finance concepts (Carr-Madan spanning formula, Tanaka formula, local time theory, last-passage time of diffusions, canonical parametrization via integral representations). However, the linear structure of the model simplifies computation significantly. Numerical implementation requires: (1) on-chain data extraction from Uniswap V3 contracts, (2) option data collection from Deribit API, (3) no-arbitrage filtering and piecewise-linear interpolation, (4) closed-form antiderivatives for IL integrals, (5) bisection for implied volatility inversion, and (6) multi-resolution partitioning. The paper provides detailed algorithms and handles edge cases (Bachelier non-elementary integrals via Gauss-Legendre quadrature). Moderate-to-high complexity due to the interplay of multiple mathematical components.

The paper provides detailed mathematical derivations, explicit formulas for intrinsic liquidity, canonical parametrization, IL replication, LVR decomposition, and implied volatility computation. Data sources are clearly specified (Deribit public API, Uniswap V3 on-chain contracts). Numerical methods are described with precision (32-point Gauss-Legendre quadrature, piecewise-linear interpolation, closed-form antiderivatives). However, no code repository is provided, and the specific data snapshots (Nov 17, 2025) would need to be re-acquired. The theoretical framework is fully self-contained with proofs.