🤖 AI Summary
This study addresses the problem of fair and efficient loss allocation under extreme market volatility in cryptocurrency futures exchanges through the automatic deleveraging (ADL) mechanism. The authors formulate ADL as a risk minimization optimization problem, deriving an optimal water-filling strategy that minimizes maximum leverage under single-asset isolated margin accounts. For multi-asset cross-margin scenarios, they introduce shadow prices and a factor model to enable scalable computation. The proposed approach is distribution-free, path-independent, and inherently resistant to wash trading and Sybil attacks. Theoretical analysis elucidates the economic rationale underlying existing queue-based ADL mechanisms and demonstrates that effectively hedged positions should undergo milder deleveraging, thereby enhancing both transparency and systemic stability.
📝 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.