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We develop a model of stable assets, including noncustodial stablecoins
backed by cryptocurrencies. Such stablecoins are popular methods for
bootstrapping price stability within public blockchain settings. We demonstrate
fundamental results about dynamics and liquidity in stablecoin markets,
demonstrate that these markets face deleveraging spirals that cause illiquidity
during crises, and show that these stablecoins have `stable' and `unstable'
domains. Starting from documented market behaviors, we explain actual
stablecoin movements; further our results are robust to a wide range of
potential behaviors. In simulations, we show that these systems are susceptible
to high tail volatility and failure. Our model builds foundations for
stablecoin design. Based on our results, we suggest design improvements that
can improve long-term stability and suggest methods for solving pricing
problems that arise in existing stablecoins. In addition to the direct risk of
instability, our dynamics results suggest a profitable economic attack during
extreme events that can induce volatility in the `stable' asset. This attack
additionally suggests ways in which stablecoins can cause perverse incentives
for miners, posing risks to blockchain consensus.

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