  Perpetual futures -- swap contracts that never expire -- are the most popular
derivative traded in cryptocurrency markets, with more than $100 billion traded
daily. Perpetuals provide investors with leveraged exposure to
cryptocurrencies, which does not require rollover or direct cryptocurrency
holding. To keep the gap between perpetual futures and spot prices small, long
position holders periodically pay short position holders a funding rate
proportional to this gap. The funding rate incentivizes trades that tend to
narrow the futures-spot gap. But unlike fixed-maturity futures, perpetuals are
not guaranteed to converge to the spot price of their underlying asset at any
time, and familiar no-arbitrage prices for perpetuals are not available, as the
contracts have no expiry date to enforce arbitrage. Here, using a weaker notion
of random-maturity arbitrage, we derive no-arbitrage prices for perpetual
futures in frictionless markets and no-arbitrage bounds for markets with
trading costs. These no-arbitrage prices provide a valuable benchmark for
perpetual futures and simultaneously prescribe a strategy to exploit divergence
from these fundamental values. Empirically, we find that deviations of crypto
perpetual futures from no-arbitrage prices are considerably larger than those
documented in traditional currency markets. These deviations comove across
cryptocurrencies and diminish over time as crypto markets develop and become
more efficient. A simple trading strategy generates large Sharpe ratios even
for investors paying the highest trading costs on Binance, which is currently
the largest crypto exchange by volume.
