Optimal Hedge Ratio for Delta-Neutral Liquidity Provision under Liquidation Constraints

Battle Count: 80

Highly relevant to quantitative trading in DeFi/crypto markets. The paper provides a rigorous analytical framework for optimal hedging of AMM liquidity positions, directly applicable to delta-neutral strategies used by sophisticated LPs. The closed-form hedge ratio formula, first-passage-time liquidation bounds, and practical rebalancing rules (15pp threshold) are immediately actionable. The finding that optimal hedge ratios cluster at 50-70% across diverse token pairs and blockchains provides robust guidance. However, the scope is limited to constant-product AMMs with collateralized borrowing, not traditional equity/futures markets.

Moderate complexity. The analytical framework requires knowledge of stochastic calculus (GBM, first-passage-time theory, moment-matching approximations). The closed-form hedge ratio formula (Theorem 4) is straightforward to implement given calibrated parameters. Monte Carlo simulation with correlated GBM paths and daily LTV checks is standard. Practical implementation requires: (1) real-time price feeds for both tokens, (2) integration with lending protocol APIs for borrowing/repayment, (3) threshold-based rebalancing logic, (4) LTV monitoring with liquidation alerts. The main complexity lies in calibrating parameters (volatilities, correlations, borrow rates, reward rates) to specific pools and maintaining them over time.

The paper provides detailed calibration parameters (Table 2), full analytical derivations (Appendices A and B), Monte Carlo simulation design (N=30,000 paths, daily steps, Cholesky decomposition), and sensitivity analyses across multiple token pairs and parameter ranges. However, no code repository is provided, and the on-chain data source (Sui blockchain, specific pool) would need to be independently sourced. The analytical framework is fully self-contained with closed-form expressions.