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

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  • Atsushi Hane

Abstract

We study the problem of optimally hedging the price exposure of liquidity positions in constant-product automated market makers (AMMs) when the hedge is funded by collateralized borrowing. A liquidity provider (LP) who borrows tokens to construct a delta-neutral position faces a trade-off: higher hedge ratios reduce price exposure but increase liquidation risk through tighter collateral utilization. We model token prices as correlated geometric Brownian motions and derive the hedge ratio h that maximizes risk-adjusted return subject to a liquidation-probability constraint expressed via a first-passage-time bound. The unconstrained optimum h* admits a closed-form expression, but at h* the liquidation probability is prohibitively high. The practical optimum h** = min(h*, h_bar(alpha)) is determined by the binding liquidation constraint h_bar(alpha), which we evaluate analytically via the first-passage-time formula and confirm with Monte Carlo simulation. Simulations calibrated to on-chain data validate the analytical results, demonstrate robustness across realistic parameter ranges, and show that the optimal hedge ratio lies between 50% and 70% for typical DeFi lending conditions. Practical guidelines for rebalancing frequency and position sizing are also provided.

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  • Atsushi Hane, 2026. "Optimal Hedge Ratio for Delta-Neutral Liquidity Provision under Liquidation Constraints," Papers 2603.19716, arXiv.org.
    • Handle: RePEc:arx:papers:2603.19716
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    References listed on IDEAS

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    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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