No-Arbitrage Pricing and Replication of Perpetual Futures

Summary

The paper derives no-arbitrage prices for perpetual futures, contracts without an expiration date whose prices are linked to spot through periodic funding payments. It treats linear, inverse, and quanto contracts in both discrete and continuous time. The central result expresses a contract’s price as a risk-neutral expectation of the spot price observed at a random time, with the timing governed by the intensity of the funding-based price anchor.

The analysis also identifies funding rules under which perpetual futures and spot prices coincide. Under those specifications, the authors show that a perpetual contract can be replicated through dynamic trading in the underlying primitive securities. These results provide a pricing framework and conditions for replication, rather than empirical evidence that a particular market’s funding mechanism follows the model. Applying the formulas in practice depends on the contract design, funding specification, and assumptions behind the no-arbitrage framework.

Key ideas

• Perpetual futures use funding payments to link futures prices to spot without a fixed expiration.
• The paper derives no-arbitrage pricing expressions for linear, inverse, and quanto contracts in discrete and continuous time.
• The futures price is represented as a risk-neutral expectation of spot sampled at a funding-dependent random time.
• Some funding specifications make perpetual futures and spot prices coincide.
• Under those specifications, dynamic trading in primitive securities can replicate the perpetual contract.

Tags

# Perpetual Futures Pricing


# Perpetual Futures Pricing









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.