While stability lasts: A stochastic model of noncustodial stablecoins

The “Black Thursday” crisis in cryptocurrency markets demonstrated deleveraging risks over-collateralized noncustodial stablecoins. We develop a stochastic model that helps explain crises these systems. In our model, the stablecoin supply is decided by speculators who optimize profitability of leveraged position while incorporating forward-looking cost collateral liquidations, which involves endogenous price stablecoin. formally characterize regimes are interpreted as stable and unstable for prove bounds on quadratic variation (QV) probability large deviations domain we demonstrate distinctly greater variance domain. identify deflationary spiral means submartingale. These spirals, resemble short squeezes, lead to faster drawdown (and potential shortfalls) accompanied higher variance, experienced Black Thursday. conclude discussing ways issues raised this paper can be mitigated.