Citation

Risk, J., Tung, S.N., Wang, T.H. “Pricing and Hedging for Liquidity Provision in Constant Function Market Making.” arXiv:2603.01344v1 [q-fin.MF] (Mar 2, 2026).

Core Contribution

Develops a canonical mathematical framework for CFMMs using price and intrinsic liquidity as coordinates (instead of token reserves). This enables:

  • Dimensional consistency across all CFMM bonding functions (Uniswap v2/v3, Balancer, Curve)
  • Streamlined approach to arbitrage-free pricing, delta hedging, and risk management

Key Technical Results

Intrinsic Liquidity

  • A single coordinate that works across all bonding curves
  • Asset reserves and value functions are linearly dependent on intrinsic liquidity
  • This linear structure makes pricing, hedging, and risk management tractable

Impermanent Loss as Options Strip

  • Characterizes IL using the Carr-Madan spanning formula
  • IL = weighted strip of vanilla options
  • Defines a fine-grained implied volatility structure for liquidity profiles
  • Enables fair value pricing of LP positions as derivatives

Path-Dependent Analysis via Last-Passage Time

  • IL is path-dependent under concentrated liquidity (Uniswap v3)
  • Last-passage time framework provides the correct characterization

Empirical Validation

  • Uniswap v3 ETH/USDC pools + Deribit option markets
  • Confirmed volatility smile consistent with crypto-asset dynamics
  • Validates the implied volatility framework for LP risk-neutral pricing

Relevance to MEV

This paper provides the mathematical foundation for understanding LP profitability — which directly affects:

  1. LVR mitigation design: knowing the exact IL/LVR as an options strip enables better hedging strategies
  2. PropAMM valuation: the intrinsic liquidity framework applies to PropAMMs with oracle-updated prices
  3. MEV protection economics: quantifying LP losses enables rational comparison of MEV protection costs vs. benefits

LVR vs. IL Distinction

This paper focuses on IL (path-independent per-position measure). The related LVR metric (introduced by Milionis et al.) is path-dependent and better captures the ongoing cost to LPs from arbitrage. The intrinsic liquidity framework connects both.