We take this question to be isomorphic to, "What Keeps Fixed Exchange Rates Fixed?" and address it with analysis familiar in exchange-rate economics. Stablecoins solve the volatility problem by pegging to a national currency, typically the US dollar, and are used as vehicles for exchanging national currencies into non-stable cryptocurrencies, with some stablecoins having a ratio of trading volume to outstanding supply exceeding one daily. Using a rich dataset of signed trades and order books on multiple exchanges, we examine how peg-sustaining arbitrage stabilizes the price of the largest stablecoin, Tether. We find that stablecoin issuance, the closest analogue to central-bank intervention, plays only a limited role in stabilization, pointing instead to stabilizing forces on the demand side. Following Tether's introduction to the Ethereum blockchain in 2019, we find increased investor access to arbitrage trades, and a decline in arbitrage spreads from 70 to 30 basis points. We also pin down which fundamentals drive the two-sided distribution of peg-price deviations: Premiums are due to stablecoins' role as a safe haven, exhibiting, for example, premiums greater than 100 basis points during the COVID-19 crisis of March 2020; discounts derive from liquidity effects and collateral concerns.

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