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Perpetual Futures Pricing

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  • 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, 2023. "Perpetual Futures Pricing," Papers 2310.11771, arXiv.org.
    • Handle: RePEc:arx:papers:2310.11771
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    References listed on IDEAS

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    1. Shiller, Robert J, 1993. "Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures," Journal of Finance, American Finance Association, vol. 48(3), pages 911-931, July.
    2. Adam K. Gehr Jr., 1988. "Undated futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 8(1), pages 89-97, February.
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