Year: 2022
Type: article
Abstract: The “Black Thursday” crisis in cryptocurrency markets demonstrated deleveraging risks in over‐collateralized noncustodial 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 (QV) 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 noncustodial ways in which the issues raised in this paper can be mitigated.
Source: Mathematical Finance
DOI: 10.1111/mafi.12357
Authors: Ariah Klages‐Mundt, Andreea Minca
Institution: Cornell University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4286698121