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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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    1. Bullmann, Dirk & Klemm, Jonas & Pinna, Andrea, 2019. "In search for stability in crypto-assets: are stablecoins the solution?," Occasional Paper Series 230, European Central Bank.
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    6. Parlatore, Cecilia, 2016. "Fragility in money market funds: Sponsor support and regulation," Journal of Financial Economics, Elsevier, vol. 121(3), pages 595-623.
    7. Marcin Kacperczyk & Philipp Schnabl, 2013. "How Safe Are Money Market Funds?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(3), pages 1073-1122.
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    Cited by:

    1. Ariah Klages-Mundt & Steffen Schuldenzucker, 2022. "Designing Autonomous Markets for Stablecoin Monetary Policy," Papers 2212.12398, arXiv.org.
    2. Shengwei You & Aditya Joshi & Andrey Kuehlkamp & Jarek Nabrzyski, 2026. "Stablecoin Design with Adversarial-Robust Multi-Agent Systems via Trust-Weighted Signal Aggregation," Papers 2601.22168, arXiv.org.
    3. Matthias Hafner & Marco Henriques Pereira & Helmut Dietl & Juan Beccuti, 2023. "The four types of stablecoins: A comparative analysis," Papers 2308.07041, arXiv.org.
    4. 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.
    5. 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.
    6. Andrey Urusov & Rostislav Berezovskiy & Yury Yanovich, 2024. "Backtesting Framework for Concentrated Liquidity Market Makers on Uniswap V3 Decentralized Exchange," Papers 2410.09983, arXiv.org.
    7. Yichen Luo & Yebo Feng & Jiahua Xu & Paolo Tasca, 2024. "Piercing the Veil of TVL: DeFi Reappraised," Papers 2404.11745, arXiv.org, revised Jul 2025.

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