A Theoretical Approach to Stablecoin Design via Price Windows

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.