While Stability Lasts: A Stochastic Model of Non-Custodial Stablecoins
This addresses risks in cryptocurrency markets for users and developers of stablecoins, but it is incremental as it builds on existing models to analyze specific crises.
The paper tackles the problem of deleveraging crises in over-collateralized non-custodial stablecoins, such as during the 'Black Thursday' event, by developing a stochastic model that characterizes stable and unstable regimes, proving bounds on price variation and demonstrating higher variance in unstable domains.
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.