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While stability lasts: A stochastic model of noncustodial stablecoins

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  • Ariah Klages‐Mundt
  • Andreea Minca

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.

Suggested Citation

  • Ariah Klages‐Mundt & Andreea Minca, 2022. "While stability lasts: A stochastic model of noncustodial stablecoins," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 943-981, October.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:4:p:943-981
    DOI: 10.1111/mafi.12357
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    References listed on IDEAS

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    Cited by:

    1. Kaihua Qin & Jens Ernstberger & Liyi Zhou & Philipp Jovanovic & Arthur Gervais, 2023. "Mitigating Decentralized Finance Liquidations with Reversible Call Options," Papers 2303.15162, arXiv.org, revised Mar 2023.
    2. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Automated Market Making: the case of Pegged Assets," Papers 2411.08145, arXiv.org.
    3. Andrey Urusov & Rostislav Berezovskiy & Yury Yanovich, 2024. "Backtesting Framework for Concentrated Liquidity Market Makers on Uniswap V3 Decentralized Exchange," Papers 2410.09983, arXiv.org.
    4. Ariah Klages-Mundt & Steffen Schuldenzucker, 2022. "Designing Autonomous Markets for Stablecoin Monetary Policy," Papers 2212.12398, arXiv.org.
    5. Matthias Hafner & Marco Henriques Pereira & Helmut Dietl & Juan Beccuti, 2023. "The four types of stablecoins: A comparative analysis," Papers 2308.07041, arXiv.org.
    6. Yichen Luo & Yebo Feng & Jiahua Xu & Paolo Tasca, 2024. "Piercing the Veil of TVL: DeFi Reappraised," Papers 2404.11745, arXiv.org, revised Jan 2025.

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