> For the complete documentation index, see [llms.txt](https://docs.paragon.trade/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.paragon.trade/markets/power-perpetuals.md).

# Power Perpetuals

A power perpetual is a perpetual futures contract on a power of an underlying asset's price. The index is $$I = P^p / K$$, where $$P$$ is the underlying's price, $$p$$ is the power, and $$K$$ is a constant fixed at launch so the index opens at the same value as the underlying. For small moves the index moves $$p$$ times as fast: a 1% move in the underlying moves a squared index 2% and a cubed index 3%. Over larger moves the power takes over. If the underlying doubles, a squared index goes up 4x and a cubed one 8x; if it halves, they fall to a quarter and an eighth. Any power above 1 adds convexity in both directions: gains grow faster than losses as a move gets larger, and longs pay shorts for that asymmetry.

The power gives options-like exposure with no strike and no expiry. The convexity that an options chain spreads across dozens of strikes and dates sits in one contract, so the liquidity that fragments across that chain can trade in a single book.

Examples on this page and the pages below use the square, $$p = 2$$.

| Instrument | Status | Underlying | Index       | Max Leverage | OI Cap | Funding Clamp | Margin Mode |
| ---------- | ------ | ---------- | ----------- | ------------ | ------ | ------------- | ----------- |
| HYPE²      | —      | HYPE       | `HYPE² / K` | 3x           | $25M   | 0.15%         | Cross       |

* **Underlying rises:** longs gain more than $$p$$ times the move. On a squared market a +10% move pays +21%.
* **Underlying falls:** longs lose less than $$p$$ times the move. On a squared market a −10% move costs −19%.
* **Underlying flat:** longs pay funding to shorts, at a rate set from the underlying's variance and financing.

**Index & payoff:** the formula, the return at any move size, and the comparison with a leveraged position rebalanced hourly. See [Index & Payoff](/markets/power-perpetuals/index-and-payoff.md).

**Funding:** why longs pay, the fair rate, and how the interest rate is set. See [Funding](/markets/power-perpetuals/funding.md).

**Hedging & risk:** delta per contract, the Greeks, and liquidation distances. See [Hedging & Risk](/markets/power-perpetuals/hedging-and-risk.md).

**Contract terms:** leverage, OI cap, and margin mode. See [Contract Specifications](/resources/specifications.md#market-specifications).

Power perpetuals were written about in 2021 by [Paradigm](https://www.paradigm.xyz/writing/power-perpetuals), [Wayne Nilsen](https://github.com/waynenilsen/zendax/blob/master/latex/PowerClaims.pdf), and [llllvvuu](https://llllvvuu.dev/blog/unbundling-gamma).


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