In this paper, we explore the short- and long-term stability of backed stablecoins offering constant mint and redeem prices to all agents. We refer to such designs as price window-based, since the mint and redeem prices constrain the stablecoin's market equilibrium. We show that, without secondary stabilization mechanisms, price window designs cannot achieve both short- and long-term stability unless they are backed by already-stable reserves. In particular, the mechanism faces a tradeoff: either risk eventual reserve depletion through persistent arbitrage by a speculator, or widen the distance between mint and redeem prices enough to disincentivize arbitrage. In the latter case, however, the market price of the stablecoin inherits the volatility of its backing asset, with fluctuations that can be proportional to the backing asset's own volatility.

翻译：本文探讨了为所有参与者提供恒定铸造与赎回价格的抵押型稳定币的短期与长期稳定性。由于铸造与赎回价格约束了稳定币的市场均衡，我们将此类设计称为基于价格窗口的机制。研究表明，在没有次级稳定机制的情况下，除非以已具备稳定性的储备资产作为抵押，否则价格窗口设计无法同时实现短期与长期稳定性。具体而言，该机制面临一个权衡：要么承担因套利者持续套利而最终耗尽储备的风险，要么通过扩大铸造与赎回价差来抑制套利行为。然而在后一种情况下，稳定币的市场价格将继承其抵押资产的波动性，其价格波动可能与抵押资产自身的波动性成正比。