Paper: arXiv 2603.15963

Authors: Steven Campbell, Natascha Hey, Ciamac C. Moallemi, Marcel Nutz

Abstract

Auto-deleveraging (ADL) mechanisms are a critical yet understudied component of risk management on cryptocurrency futures exchanges. When available margin and other loss-absorbing resources are insufficient to cover losses following large price moves, exchanges reduce positions and socialize losses among solvent participants via rule-based ADL protocols. We formulate ADL as an optimization problem that minimizes the exchange’s risk of loss arising from future equity shortfalls. In a single-asset, isolated-margin setting, we show that under a risk-neutral expected loss objective the unique optimal policy minimizes the maximum leverage among participants. The resulting design has a transparent structure: positions are reduced first for the most highly levered accounts, and leverage is progressively equalized via a water-filling (or ``leverage-draining’’) rule. This policy is distribution-free, wash-trade resistant, Sybil resistant, and path-independent. It provides a canonical and implementable benchmark for ADL design and clarifies the economic logic underlying queue-based mechanisms used in practice. We further study the multi-asset, cross-margin setting, where the ADL problem becomes genuinely multi-dimensional: the exchange must allocate a vector of required reductions across accounts with portfolios exposed to correlated price moves. We show that under an expected-loss objective the problem remains separable across accounts after introducing asset-level shadow prices, yielding a scalable numerical method. We observe that naive gross leverage can be misleading in this context as it ignores hedging within portfolios. When asset prices are driven by a single dominant risk factor, the optimal policy again takes a water-filling form, but now in a factor-adjusted notion of leverage, so that more effectively hedged portfolios are deleveraged less aggressively.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation of auto-deleveraging (ADL) using constrained optimization, duality, and water-filling algorithms for both isolated and cross-margin settings. While it introduces a highly novel and mathematically sound framework for crypto market design, it lacks empirical backtesting against real historical liquidations or market orderbook data.

Research Flowchart

  flowchart TD
    Goal["Research Goal: Formulate optimal Auto-Deleveraging (ADL) mechanism to minimize exchange equity shortfalls"] --> Inputs["Inputs: Trader portfolios, margin levels, and asset correlation matrix"]
    Inputs --> Framework["Formulate ADL as Expected Loss Minimization Problem"]
    
    Framework --> SingleAsset["Single-Asset / Isolated Margin Setting"]
    Framework --> MultiAsset["Multi-Asset / Cross-Margin Setting"]
    
    SingleAsset --> SingleOutcome["Optimal Policy: Equalize maximum leverage via 'Leverage-Draining' (Water-Filling)"]
    MultiAsset --> MultiOutcome["Optimal Policy: Factor-Adjusted Leverage Draining (Accounts for Hedging/Shadow Prices)"]
    
    SingleOutcome & MultiOutcome --> KeyProperties["Key Properties: Sybil-resistant, Wash-trade resistant, Distribution-free"]