Paragon Launches Power Perps to Offer New Volatility Trading Strategies

Author: 0xFacai, BlockBeats

We previously mentioned that in September, the notional volume of on-chain options reached $4.829 billion, a 121.7% month-over-month increase; the monthly premium volume also rose from just over $20 million at the beginning of the year to over $80 million. Hyperliquid founder Jeff has publicly discussed the development opportunities in options.

However, many crypto-native traders are already accustomed to trading perpetual contracts: go long when bullish, go short when bearish, deposit margin, and open or close positions at any time. Switching to the options interface, they’re faced with rows of strike prices, expiration dates, and Greek letters—by the time they process the complexity, half their trading impulse is already drained.

HIP-3 exchange Paragon has recently launched Power Perps, offering another entry point—it begins with HYPE², allowing traders to achieve option-like payoff curves through contract trading.

No strike price, no expiration date. You're still trading a perpetual contract, but the price it tracks is now the square of HYPE.

Convexity

The profit and loss of a standard perpetual contract is a straight line. Holding a fixed number of long positions means you gain the same amount for every $1 increase in the underlying asset, and lose the same amount for every $1 decrease. Leverage makes this line steeper, but the shape remains unchanged.

The Nth power contract changed this.

For ease of calculation, assume that an asset's price is $100 at listing, and the quadratic contract price also starts at 100.

When the underlying rises to 110, the index reaches 121, a 21% increase; when the underlying falls to 90, the index drops to 81, a 19% decline. With the same 10% price movement, long positions gain slightly more on the upside and lose slightly less on the downside.

Expanding the leverage makes the differences more pronounced. If the underlying asset rises by 50%, the squared index rises by 125%; if the underlying asset falls by 50%, the index falls by 75%. If the underlying asset doubles, the index becomes four times its original value. With a cubed contract, the effect is even greater: if the underlying asset doubles, the index becomes eight times its original value.

Assume the underlying asset's price change is r:

The price change of a quadratic contract = 2r + r²

The previous 2r provides the return magnitude for a 2x leveraged long position; the subsequent r² is always non-negative regardless of price movement, thus increasing returns during upward trends and reducing losses during downward trends compared to a 2x long position, with the difference becoming larger as market volatility increases.

This is "convexity." Moving up along the quadratic curve, each additional dollar increase in price yields greater profits for long positions than the previous dollar; moving down, each additional dollar decrease results in smaller losses than the previous dollar. The sensitivity of quadratic contracts automatically adjusts with price—a feature ordinary contracts cannot achieve.

Options traders are willing to buy precisely this kind of "convexity."

The concept had a theoretical foundation as early as 2021. Paradigm's Everlasting Options explored how to maintain "perpetual" option exposure using continuous funding fees, and the subsequent Power Perpetuals article proposed using the power of price as the tracking target. Opyn later implemented this with Squeeth, which tracks ETH², and Paragon aims to bring such products to Hyperliquid's order book.

In addition, traditional options trading demand is spread across many contracts with different strike prices and expiration dates, resulting in highly fragmented liquidity. "Nth-power contracts" allow traders of the same underlying asset and same power to share a single order book.

Fees

Seeing this, it’s easy to wonder: if quadratic contracts rise faster and fall slower, where is the cost of this advantage?

We conduct an experiment with a long-short double position. Suppose a trader simultaneously opens a quadratic long position and hedges it with a linear short position using two units of the underlying asset, both at a price of 100. When the underlying asset price rises from 100 to 110, the quadratic long position gains 21, while the linear short position loses 20, resulting in a net profit of 1. When the underlying asset price falls from 100 to 90, the quadratic long position loses 19, while the linear short position gains 20, again resulting in a net profit of 1. When the price reaches 120 or drops to 80, the net profit in both cases is 4.

The profit and loss of this long-short portfolio can be expressed as:

Long-short portfolio profit and loss = (Underlying asset price minus 100) squared divided by 100

Without funding rates, traders could exploit the above method to arbitrage for free.

However, the no-arbitrage principle requires that such benefits must have a price—that is, the funding rate.

It’s easier to understand if you think from the market maker’s perspective. The market maker sells one unit of the quadratic contract while buying two units of the underlying asset to hedge. If the underlying rises by $10, the market maker loses $21 on the short position but only gains $20 from the spot hedge, resulting in a net loss of $1. If the underlying falls by $10, the market maker gains $19 on the short position but loses $20 on the spot hedge, again resulting in a net loss of $1. This is precisely the “arbitrage” profit on the other side.

Market makers must continuously adjust their hedge positions as prices change. After each adjustment, the next price movement generates a profit or loss related to the square of the price change. Summing these squared movements gives the "variance" here. The more violently the price fluctuates, the higher the hedging cost market makers bear for providing convexity.

Therefore, in addition to the holding cost of regular contracts, long positions in N-th power contracts must continuously pay for convexity. This cost is related to variance (the square of volatility) and is typically paid by longs to shorts. The premium or discount in the order book also affects the final funding rate.

Liquidation

Start with $100, using $100 as principal, and compare a 2x long position with a quadratic long position fully collateralized at $100.

When the underlying asset drops from 100 to 50, a 2x long position loses $100, exhausting the entire principal, and liquidation would actually occur even earlier. Ignoring funding rates and losses from other cross-margin positions, a squared long position dropping from 100 to 25 still retains $25 in equity and would not be liquidated solely due to the price decline.

Fully collateralized quadratic longs give traders approximately double the initial price sensitivity while protecting against liquidation from simple price declines.

However, adding leverage to a quadratic contract brings liquidation closer rapidly. According to Paragon’s risk documentation example, ignoring accumulated funding fees and other account assets, a 2x HYPE² long position will be liquidated if HYPE drops by approximately 22.5%, while a 3x HYPE² long position will be liquidated with just a 10.6% decline.

The short side must be even more cautious. The higher the price rises, the faster the squared shorts lose value, and 1x squared shorts will also be liquidated.

Volatility trading

The combination of a quadratic long position paired with a linear short position can also be turned into a trading strategy. You don’t need to predict whether the price will go up or down next—just determine whether it will move far enough away from its current level.

In traditional options, buying a call and a put option with the same strike price and expiration date creates a "straddle." The call profits when prices surge, while the put profits when prices plunge, offering profit potential in both directions. Power Perps achieve a similar upward-sloping payoff curve on both sides by combining a quadratic long position with a linear short position.

This is an intuitive entry point for going long on volatility. Both large price increases and decreases can create opportunities, but sufficient price movement is needed to offset funding costs.

Conversely, shorting the quadratic contract and buying the corresponding amount of the underlying asset or a linear long position to hedge allows you to short volatility. If the price remains near the entry level, the funding fees collected by the quadratic short contract can become profit; however, if the price moves significantly up or down, the hedged losses will increase proportionally to the square of the price movement.

However, the fact that quadratic contracts have no expiration date means that funding fees, as a holding cost, can accumulate indefinitely.

Power Perps cannot replicate all traditional options strategies exactly. Straddles require two different strike prices; spreads can set upper and lower limits on profit and loss through different strike prices; covered calls and covered puts also require selling options at specified strike prices to give up part of the potential gain in one direction in exchange for premium.

These strategies have payoff inflection points defined by strike prices and typically specify an expiration time. Combining quadratic contracts with linear positions results in a smooth curve. Adjusting position ratios can approximate certain option strategies within a specific price range; however, to precisely define conditions such as “capping gains at a certain price” or “maintaining constant returns within a specific range,” options are still necessary.

The cost of simplified operations and centralized liquidity is a reduction in the variety of freely selectable yield structures.

The Evolution of the Listing Strategy

Hyperliquid provides an order book, underlying markets, and a margin system, while Paragon builds upon these to design new yield curves. Market makers can hedge more easily, and developers can continue packaging strategies, reducing the need for traders to manually construct and adjust positions.

Traditional options have demonstrated that the market has a long-standing demand for diverse payoff structures. The value of Paragon’s attempt lies in expressing part of this demand in a way familiar to crypto-native traders, while also enabling existing perpetual liquidity to hedge the new product.

A more significant trend is that "listings" on HIP-3 exchanges have evolved from selecting popular traditional financial assets to creating new forms of derivatives. We look forward to seeing more such financial innovations on Hyperliquid.