Perpetual future pricing

Damien Ackerer, Julien Hugonnier and Urban Jermann

No 19455, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: Perpetual futures are contracts without expiration date in which the anchoring of the futures price to the spot price is ensured by periodic funding payments from long to short. We derive explicit expressions for the no-arbitrage price of various perpetual contracts, including linear, inverse, and quantos futures in both discrete and continuous-time. In particular, we show that the futures price is given by the risk-neutral expectation of the spot sampled at a random time that reflects the intensity of the price anchoring. Furthermore, we identify funding specifications that guarantee the coincidence of futures and spot prices, and show that for such specifications perpetual futures contracts can be replicated by dynamic trading in primitive securities.

Keywords: Cryptocurrencies; Derivatives (search for similar items in EconPapers)
JEL-codes: E12 G13 (search for similar items in EconPapers)
Date: 2024-09
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