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Hedging That Needs Continuous Probability - article banner

Introduction

Most prediction market events resolve either a YES or NO. Major platforms such as Polymarket, Kalshi, and Opinion run thousands of markets like "Will BTC be up or down on day XYZ?". For that kind of question, they work fine. But many builders want to price non-binary events. Earnings forecasts, macro hedges (GDP, CPI, inflation), or commodity exposure are numeric and best expressed as a number on a scale, not a YES or a NO.

This piece uses Polymarket's March 2026 oil markets dataset to illustrate what happens when binary architecture is asked to represent a continuous outcome. The platform ran 21 separate markets (>$90, >$100, >$105 etc.) on where crude oil futures (CL) would settle at month-end.

Polymarket crude oil March 2026 - total volume by strike. Bar chart showing volume concentration around round-number strikes, with the $100 strike highlighted.

Figure 1. Polymarket crude oil March 2026 - total volume by strike. The HIGH markets ask "will it exceed $X?", LOW markets ask "will it fall below $X?".

Three patterns:

  • Top five strikes capture 52% of total volume.
  • Top ten strikes capture 80% of total volume.
  • The remaining fifteen markets share 20% of total volume.

Most strikes are illiquid and depth lives in a handful of contracts.

Volume clusters at round-number strikes (like $90, $100, $110) due to round-number bias. The $100 strike alone captured $15.7m in volume, while the $95 strike attracted only $3.1m volume - a 5x difference. The pattern appears frequently around where the futures contract is trading.

A hedger whose belief lands at $107 has nowhere natural to express it. The available depth sits at $105 or $110 and the hedger either narrows the band to fit or accepts a larger band, incurring a spread cost they didn't budget for.

HIGH markets - Yes/No trading volume by strike. Asymmetric distribution across the strike ladder.

Figure 2. HIGH markets - Yes/No trading volume by strike.

LOW markets - Yes/No trading volume by strike. Same asymmetry in the opposite direction.

Figure 3. LOW markets - Yes/No trading volume by strike. Source: Dune query.

Breaking down both HIGH and LOW markets, the volume distribution between YES and NO is asymmetric across the strike ladder. The $200 (HIGH) strike market took in $13.5m in NO volume against $300k in YES. The $40 strike shows the same pattern in the opposite direction. At the far end, traders are collecting premiums on near-certain outcomes - functionally low-risk yield trades.

Around strike $90 to $120, there is real two-sided trading with decent YES and NO volumes. The rest looks more like yield-collection trades.


Binary architecture

The liquidity fragmentation isn't unexpected - it is what binary contracts produce when applied to a continuous outcome. For a builder, the practical consequence is that binary outcome architecture can't cleanly express continuous belief, and the cost shows up in product-level friction.

The clearest place where this surfaces is hedging.

Hedging linear oil exposure - continuous payoff vs 5-strike binary staircase. Smooth diagonal loss curve versus stepped binary payoff, with basis risk gaps highlighted in yellow.

Figure 4. Hedging linear oil exposure: continuous payoff vs 5-strike binary staircase.

Assume:

  • a small hedger trying to hedge continuous oil cost exposure
  • fuel cost scales linearly with oil price
  • the firm has to construct a payoff that matches their loss curve as fuel cost increases

On any platform, you are buying multiple binary contracts at different strikes and stitching their payoffs together. The result is a staircase where the hedge pays nothing and then jumps at each strike crossing, staying flat before jumping again. The trader's loss is smooth while the hedge isn't. The basis risk mismatch (highlighted in yellow above) shows no amount of additional strikes eliminates it. You could add more strikes between them, but that would add execution cost at every strike.

Binary events are suitable for binary contracts. However, when applied to a continuous outcome, they produce a staircase approximation - and that approximation comes at a cost. The hedger is paying more for the granular level of hedging.

To illustrate, a hedger who needs coverage at $107 has two choices on a binary-based platform: (1) buy the $105 contract, or (2) buy the $110 contract. If they buy $105, they are hedged up to $105 but exposed for every dollar oil rises beyond that until the $110 strike triggers. If they buy $110, the contract only pays if oil exceeds $110, leaving them fully uncovered if oil settles at $107. There is no contract at $107.

The hedger either overpays for coverage they don't need or accepts a gap in the range they actually care about. With $5 strike spacing on a $20 range, that gap can represent up to 25% of total hedge value. A continuous market eliminates this - the hedger draws their range directly, the protocol settles against the actual price, and there is no strike to miss.


How continuous probability fills the gap

A continuous market reframes the question from "did it cross the strike" to "where will the futures spot price land". The structure prices that single question as a single market. The hedger doesn't pick a strike. They choose to hedge across a price range (narrow if they're confident, wider if they aren't) and the protocol settles their position against the actual settlement price. A single market where liquidity and payout functionalities are merged.

The hedger's position as a shape over oil prices - a flat region from $90 to $110 expressing the desired payout across price range.

Figure 5. The hedger's position: a shape over oil prices.

Our hedger can hedge fuel cost by buying into a continuous probability market that collapses the 21-market problem into one position. They draw a flat region from $90 to $110 instead of legging into five binary strikes - expressing the desired payout across the price range directly.

The market's probability distribution remains shaped by the majority. Each trader's capital contributes to the same shape. There are no thresholds to cluster around and no fragmentation across strikes.

functionSPACE's protocol is one implementation. The mechanism prices each position by how much it reshapes the market's overall density and provides smooth payoffs and consistent pricing without needing market makers or external subsidies.

The diagram below shows this continuous outcome architecture running in a test environment in functionSPACE.

WTI Crude Oil Price (USD/bbl) by March 31st 2026 - probability density with a main peak around $90 falling off smoothly to the right.

Figure 6. WTI Crude Oil Price (USD/bbl) by March 31st 2026, expressed as a continuous shape.

The shape has one main peak around $90, reflecting where the market expresses a view on where oil will land. The probability density falls off smoothly to the right. The architectural point stands - one normally distributed shape.


How builders can ship the hedging vertical today

The implementation is more compact than most builders expect. Three components do the work:

  • A smart-contract layer that holds the current density. This is where the shape lives on-chain and gets updated as traders place positions.
  • A front-end shape editor. Users draw regions across a price range - a flat block for a hedge, a peaked curve for a directional view - instead of buying yes or no on individual strikes.
  • A single numeric oracle for settlement. When the market resolves, one number determines payouts across every position in the pool.

That's the whole stack.


Limitations

Three things to consider before committing.

UI complexity. A UI for the masses would require more sophisticated visualisation and more thought about how a trader expresses a "shape of belief".

Depth is a participation problem. A continuous market collapses numerous binary contracts into one shape, but aggregate depth still depends on participants showing up and adding liquidity into the pool. A continuous market with thin participation will still be a thin market.

Binary contracts are still better for binary questions. If the question really is yes-or-no - will a bill pass, did an event happen, did a metric cross a single threshold - binary contracts are categorically better. They are well understood and users don't need to reason about distributions. Continuous markets aren't a replacement.


Conclusion

The March 2026 oil futures case study shows how continuous probability prices outcomes without fragmenting capital across strikes. Hedging produces smooth payoffs instead of staircase payoffs. Continuous probability markets solve this with one market, one liquidity pool, and a single numeric settlement.

The question for builders isn't "should we use prediction markets?" It's "is the outcome we're trying to price binary?". Binary outcomes remain ideal for direct yes-or-no questions. Continuous probability is the right primitive to consider for numeric outcomes.