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Perpetual Futures Pricing

Author

Listed:
  • Damien Ackerer
  • Julien Hugonnier
  • Urban Jermann

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.

Suggested Citation

  • Damien Ackerer & Julien Hugonnier & Urban Jermann, 2024. "Perpetual Futures Pricing," NBER Working Papers 32936, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:32936
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    Cited by:

    1. Jaehyun Kim & Hyungbin Park, 2025. "Designing funding rates for perpetual futures in cryptocurrency markets," Papers 2506.08573, arXiv.org.
    2. Tarun Chitra & Theo Diamandis & Nathan Sheng & Luke Sterle & Kamil Yusubov, 2025. "Perpetual Demand Lending Pools," Papers 2502.06028, arXiv.org, revised May 2025.

    More about this item

    JEL classification:

    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian; Modern Monetary Theory
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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