Citation

Hane, A. “Optimal Hedge Ratio for Delta-Neutral Liquidity Provision under Liquidation Constraints.” Independent researcher. arXiv:2603.19716v1 [q-fin.PM] (Mar 2026).

Core Problem

An LP in a constant-product AMM who wants to hedge price exposure via collateralized borrowing (delta-neutral strategy) faces a tradeoff:

  • Higher hedge ratio → lower price exposure (reduced IL/LVR)
  • Higher hedge ratio → tighter collateral utilization → higher liquidation risk

This paper derives the optimal hedge ratio h balancing these effects.

Model

  • Token prices: correlated geometric Brownian motions
  • Hedge funded by collateralized borrowing from a DeFi lending protocol (e.g., Aave, Compound)
  • LTV constraint: loan-to-value ratio must stay below liquidation threshold

Main Results

  1. Unconstrained optimal hedge ratio h* has a closed-form expression
  2. The constraint binds: at h*, the liquidation probability is prohibitively high in practice
  3. Practical optimum h = min(h*, h_bar(ε)) where h_bar(ε) is the binding liquidation constraint threshold, characterized via first-passage-time analysis
  4. Optimal range: h lies between 50% and 70% for typical DeFi lending conditions
  5. Rebalancing: optimal rebalancing frequency and position sizing guidelines provided

Practical Implications

  • Full delta-hedging (h=1.0) dramatically increases liquidation risk; most practitioners should hedge 50–70%
  • The 50–70% range is insensitive to the specific collateral token pair (validated across multiple pools)
  • Under high volatility regimes, the constraint tightens → optimal hedge ratio falls

Relevance to MEV/Searchers

This paper is primarily a DeFi portfolio management paper. MEV relevance:

  • LP strategies: LPs who also engage in MEV protection (hedging LVR) benefit from this framework
  • Liquidation MEV: over-leveraged LP positions create liquidation opportunities; this paper models when LPs become vulnerable to liquidation-MEV extraction