Arbitrage in Perpetual Contracts

Abstract

Perpetual contracts, designed to track the underlying price through a funding swap mechanism, have gained significant popularity in cryptocurrency markets. However, observed price discrepancies between perpetual contracts and the underlying asset cannot be explained solely by transaction fees. By examining the impact of the clamping function inherent in the funding swap mechanism -- an overlooked aspect in existing literature -- we derive model-free no-arbitrage bounds for perpetual contracts. Our findings reveal that these bounds persist as intervals even without transaction fees, due to the clamping function. Empirical analysis using two years of Binance data supports the validity of our proposed bounds.