Traditional futures contracts have maturity dates, upon which the futures price converges to the spot price. In the cryptocurrency market, the most popular contracts do not have a maturity date. They’re called perpetual contracts. Unlike fixed-maturity futures, perpetuals do not expire. This feature enhances the liquidity of the contract. Because they have no set expiration date, perpetuals are not guaranteed to converge to the spot price of their underlying asset at any given time, and the usual no-arbitrage pricing formulas do not apply.
To minimize the gap between perpetual futures and spot prices, long position holders periodically pay short position holders a funding rate proportional to this gap, incentivizing trades that help narrow it. Typically, the funding rate is paid every eight hours and approximately equals the average futures-spot spread over the preceding eight hours.
How do you price a perpetual contract, given that the usual no-arbitrage condition does not apply?
Reference [1] proposed the use of random-maturity arbitrage to price perpetual futures. Basically, random-maturity arbitrage generalizes traditional arbitrage by allowing for a positive payoff at an uncertain future time. The authors also developed bounds for the random-maturity arbitrage price and used these bounds to construct an arbitrage strategy that delivered a high Sharpe ratio. They pointed out,
In an ideal, frictionless world, we show that arbitrageurs would trade perpetual futures in such a way that a constant proportional relationship would hold between the futures price and the spot price. In the presence of trading costs, the deviation of the futures price from the spot would lie within a bound.
Motivated by our theory, we empirically examine the comovement of the futures- spot spread across different cryptocurrencies and implement a theory-motivated arbitrage strategy. We find that this simple strategy yields substantial Sharpe ratios across various trading cost scenarios. The evidence supports our theoretical argument that perpetual futures-spot spreads exceeding trading costs represent a random-maturity arbitrage opportunity.
Finally, we provide an explanation for the common comovement in futures-spot spreads across different crypto-currencies: arbitrageurs can only accommodate market demand if the price deviation exceeds trading costs. As a result, the overall sentiment in the futures market relative to the spot market is reflected in the spread. Our empirical findings suggest that past return momentum can account for a significant portion of the time-series variation in the futures-spot spread.
An interesting conclusion of the paper is that overall sentiment in the futures market relative to the spot market is reflected in the spread. Empirical findings suggest that past return momentum accounts for a significant portion of the time-series variation in the futures-spot spread.
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References
[1] He, Songrun and Manela, Asaf and Ross, Omri and von Wachter, Victor, Fundamentals of Perpetual Futures (2022). https://ssrn.com/abstract=4301150
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