Power Perpetuals: Convex Exposure, Funding, and Pricing Constraints

Summary

The paper introduces power perpetuals, derivatives indexed to a power of an underlying asset’s price. Because a power above one creates convex exposure, gains and losses respond asymmetrically to price moves. Long holders pay a periodic premium yield to shorts based on the difference between the traded contract price and its power-based index. The instrument offers options-like exposure without a strike or expiry, but this exposure carries an ongoing funding cost.

For valuation, the authors adapt a framework for perpetual derivatives: price an expiring power claim under Black–Scholes assumptions, then combine claims across maturities. The resulting series converges only for suitable combinations of power, volatility, and funding interval; choosing a shorter interval can address the stated convergence issue. Examples discuss squared and cubed Ether contracts. The pricing discussion is illustrative and relies on simplifying assumptions, so it does not establish market prices or realized trading performance.

Key ideas

• A power perpetual tracks a power of an underlying asset price and can provide convex exposure.
• Long positions pay periodic premium yield to short positions based on the mark-to-index difference.
• The proposed valuation combines expiring power claims under Black–Scholes assumptions into a perpetual structure.
• The valuation series may fail to converge for some combinations of contract power, volatility, and funding interval.
• The examples illustrate Ether-based contracts but do not provide evidence of trading performance.

Tags

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