当稳定持续时：非托管稳定币的随机模型
While Stability Lasts: A Stochastic Model of Non-Custodial Stablecoins
摘要：
加密货币市场的“黑色星期四”危机表明了过度抵押的非托管稳定币的去杠杆化风险。我们开发了一个随机模型，有助于解释这些过度抵押系统的去杠杆化危机。在我们的模型中，稳定币供应由投机者决定，他们优化杠杆头寸的盈利能力，同时考虑抵押品清算的前瞻性成本，这涉及稳定币的内生价格。我们正式描述了被解释为稳定币稳定和不稳定的政权。我们证明了二次变异的界限和稳定域中大偏差的概率，我们证明了在不稳定域中明显更大的价格方差。我们确定了一个通货紧缩的去杠杆化螺旋通过下鞅。这些去杠杆化螺旋，类似于空头挤压，导致更快的抵押品缩减（和潜在的短缺），并伴随着更高的价格差异，就像黑色星期四所经历的那样。最后，我们讨论了非监禁的方式，在本文中提出的问题可以减轻。
英文摘要：
The `Black Thursday' crisis in cryptocurrency markets demonstrated deleveraging risks in over-collateralized non-custodial stablecoins. We develop a stochastic model that helps explain deleveraging crises in these over-collateralized systems. In our model, the stablecoin supply is decided by speculators who optimize the profitability of a leveraged position while incorporating the forward-looking cost of collateral liquidations, which involves the endogenous price of the stablecoin. We formally characterize regimes that are interpreted as stable and unstable for the stablecoin. We prove bounds on quadratic variation and the probability of large deviations in the stable domain and we demonstrate distinctly greater price variance in the unstable domain. We identify a deflationary deleveraging spiral by means of a submartingale. These deleveraging spirals, which resemble short squeezes, lead to faster collateral drawdown (and potential shortfalls) and are accompanied by higher price variance, as experienced on Black Thursday. We conclude by discussing non-custodial ways in which the issues raised in this paper can be mitigated.
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