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A Taxonomy of Event-Linked Perpetual Futures: Variant Designs Beyond the Single-Market Binary Case

This paper presents a formal taxonomy of seven canonical variants of event-linked perpetual futures beyond the single-market binary case, analyzing their unique payoff structures, design constraints, and inheritance from a foundational risk framework across four orthogonal design axes.

Original authors: Maksym Nechepurenko

Published 2026-05-12

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Maksym Nechepurenko

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a machine that bets on whether a specific event will happen, like "Will it rain tomorrow?" or "Will Candidate X win the election?" In the world of prediction markets, this is a standard bet. But what if you wanted to bet on these events using a special kind of "perpetual" contract—a bet that never truly ends, where you pay a small fee to keep your position open, similar to how you might pay interest to hold a stock?

Paper 1 of this research series built the blueprint for the simplest version of this machine: a bet on a single "Yes/No" event.

This paper (Paper 2) says, "Wait, the world is more complicated than just one Yes/No question." It argues that if you try to build more complex betting machines based on that simple blueprint without a new map, you will break things. So, the author has drawn a Taxonomy—a detailed family tree—of seven new types of these perpetual betting contracts.

Think of the original contract as a single-lane road. This paper explores what happens when you try to build intersections, roundabouts, and multi-lane highways.

Here are the seven new "vehicles" (variants) the paper introduces, explained with simple analogies:

1. The Conditional Bet (The "If-Then" Machine)

The Concept: Instead of betting on "Will it rain?", you bet on "Will it rain IF the temperature is above 80 degrees?"
The Analogy: Imagine a vending machine that only dispenses a soda if you insert a coin and the machine is plugged in. If the machine isn't plugged in (the condition fails), the whole transaction is undefined.
The Paper's Warning: If the "plugged-in" condition becomes very unlikely (the denominator gets tiny), the math breaks down. The machine becomes unstable and hard to price before the event even happens.

2. The Event Spread (The "Race" Machine)

The Concept: Betting on the difference between two events. "How much more likely is Candidate A to win compared to Candidate B?"
The Analogy: Imagine betting on the margin of victory in a horse race. You aren't betting on who wins; you are betting on the gap between the first and second place.
The Paper's Warning: This is tricky because the two horses might finish at different times. If Horse A finishes first, you are left waiting for Horse B. The paper notes you need a special "three-channel" safety system to handle the risk of the first horse finishing while the second is still running.

3. The Event Basket (The "Smoothie" Machine)

The Concept: Betting on a weighted mix of many events. "What is the average probability that any of these 10 candidates win?"
The Analogy: Instead of betting on one specific fruit, you buy a smoothie made of 10 different fruits. The taste (the outcome) is a mix.
The Paper's Warning: If one fruit in the smoothie is bad (resolves poorly), it affects the whole drink. If all the fruits are bad at the exact same time, the smoothie collapses. The paper says you need a special margin system that accounts for the fact that all the fruits might rot simultaneously.

4. The Volatility/Entropy Bet (The "Chaos" Machine)

The Concept: Betting not on what happens, but on how much the odds swing before it happens.
The Analogy: Imagine a weather forecast. Most bets are on "Will it rain?" This bet is on "How much will the forecast change its mind between today and tomorrow?"
The Paper's Warning: This is the most different machine. It doesn't crash to a "Yes" or "No" at the end; it just keeps churning. It behaves more like a standard stock market derivative than a prediction market bet. The old safety rules don't apply here.

5. The Liquidity Index (The "Traffic" Machine)

The Concept: Betting on how easy it is to trade in the market itself (how wide the spreads are, how deep the order books are).
The Analogy: Instead of betting on the price of a car, you are betting on how crowded the car dealership is. Are there lots of buyers and sellers, or is it a ghost town?
The Paper's Warning: This is a "meta" bet. It's very hard to define what "traffic" means, and it's easy to manipulate. If you bet on the traffic, you might accidentally cause the traffic to change just by being there. The paper says this is too theoretical to build right now.

6. The Rolling Event (The "Season Pass" Machine)

The Concept: A perpetual bet that automatically switches from one event to the next. "Bet on the next Fed meeting, then automatically switch to the one after that."
The Analogy: Imagine a subscription service. You don't buy a ticket for one specific movie; you buy a pass that gives you the next movie in the queue, then the one after that, forever.
The Paper's Warning: The paper says this works well for regular events (like monthly economic reports) but is impossible for one-off events (like a specific election). It requires a lot of data over a long time to test properly.

7. The Funding-Only Derivative (The "Rent" Machine)

The Concept: A contract that never settles. You never get a final payout based on an event. You only earn or pay fees (funding) based on the disagreement between traders.
The Analogy: Imagine a landlord who never sells the house. They just collect rent based on how much the neighborhood is arguing about the property value.
The Paper's Warning: This is the most experimental. There is no final "score." It's purely about the flow of money between traders. The paper says we don't even know if anyone would want to use this yet.

The Big Takeaway

The author's main point is that you cannot just copy-paste the rules from the simple "Yes/No" bet to these complex machines.

The Blueprint: The paper provides a "Inheritance Map." It tells engineers which safety features from the simple bet work for the complex ones, which ones need to be modified, and which ones must be thrown away entirely.
The Reality Check: The paper admits that none of these seven complex machines have been built or tested in the real world yet. They are theoretical designs.
The Goal: The purpose of this paper is to give researchers and builders a common vocabulary. Before they try to build these complex betting machines, they need to know exactly which "engine" (risk design) they are using, because a machine built for a "Race" (Spread) will crash if you try to drive it like a "Smoothie" (Basket).

In short, this paper is a design manual for the next generation of prediction market tools, warning builders that "one size does not fit all" and providing the specific instructions needed for each new type of tool.

Technical Summary: A Taxonomy of Event-Linked Perpetual Futures

Problem Statement
Event-linked perpetuals are a structurally novel class of derivatives where the underlying asset tracks prediction-market event prices, conditional probabilities, event baskets, or resolution states. While Paper 1 of this research programme (Nechepurenko, 2026d) established a resolution-aware risk-design framework (PIRAP) for the simplest case—a single binary prediction-market probability—the instrument class is significantly broader. Practitioners and researchers have proposed variants involving conditional probabilities $P(A|B)$ , event spreads, weighted baskets, volatility derivatives, and funding-only structures.

The core problem addressed is that these variants are structurally distinct but often treated interchangeably in literature and informal discussion. Crucially, the risk-engineering requirements of these variants differ in ways that the single-market binary case does not expose. Without a formal taxonomy, both research and practice operate in a vocabulary that conflates structurally different objects, leading to potential misapplication of risk frameworks (e.g., margin and funding rules) that do not uniformly carry over from the single-market case. Furthermore, empirical evaluability varies significantly across variants, with some requiring multi-platform data or multi-week archives not present in existing datasets.

Methodology
This paper develops a formal taxonomy of seven "pure-form" canonical variants beyond the probability-index perpetual. The analysis is organized along four orthogonal design axes:

Underlying Geometry: The real-valued quantity tracked (e.g., single probability, conditional probability, spread, basket, volatility/entropy, liquidity index).
Temporal Structure: Whether the contract is anchored to a single fixed resolution, a sequence of recurring events, or a perpetually existing process.
Settlement Structure: Whether the contract settles at terminal collapse, rolls over, or carries no settlement leg (funding-only).
Venue Composition: Whether underlyings are drawn from a single venue or multiple platforms.

For each of the seven variants, the paper provides:

Formal Definitions: Precise specifications of the underlying process, payoff structure, settlement rules, and boundary behavior.
Inheritance Mapping: A systematic analysis of which components of the Paper 1 framework (bounded-event process model, terminal collapse properties, non-portability propositions, margin/funding/resolution-zone protocols) apply directly, require modification, or fail entirely.
Design Constraints: Identification of variant-specific constraints, such as oracle composition rules, leg-resolution ordering, and weight normalization.
Microstructure Analysis: Characterization of basis formation channels (single-leg vs. cross-leg), liquidity coupling, and manipulation surfaces.
Evaluability Criteria: Explicit determination of whether a variant's underlying is observable on the PMXT v2 archive, requires multi-platform data, or requires multi-week archives.

The paper is primarily theoretical. It does not conduct full counterfactual replay or empirical evaluation of the new variants, noting that such work requires future data extensions or deployment.

Key Contributions

Formal Taxonomy: The paper enumerates and defines seven variants:
- B. Conditional Probability: $P(A|B)$ , inheriting bounded support but introducing denominator instability risks.
- C. Event Spread: $p(A) - p(B)$ , inheriting bounded support but requiring three-channel resolution risk decomposition.
- D. Event Basket: Weighted sum of probabilities, inheriting bounded support but requiring multi-period jump-aware margin.
- E. Volatility/Entropy: Variance or entropy of the probability process, departing from terminal collapse and requiring continuous-underlying treatment.
- F. Liquidity Index: Derivative on microstructure metrics (spread/depth), acting as a meta-market with reflexive feedback.
- G. Rolling Event: Continuous succession of contracts on recurring events, addressing the "perpetual on expiring event" tension.
- H. Funding-Only: Exposure to funding flows without settlement, acting as an exposure-without-settlement structure.
Inheritance Maps: The paper provides a granular map (Table 3) detailing how Paper 1's framework components (e.g., jump-aware tiered margin, resolution-zone protocols, non-portability propositions) apply to each variant. Notable findings include:
- Variants B, C, and D largely inherit the bounded-event process model and terminal collapse properties, but require adaptations for oracle composition and leg-resolution ordering.
- Variant E (Volatility/Entropy) escapes the terminal collapse risk of Proposition 1 but introduces deterministic decay risks (for entropy) and requires re-derivation of boundary-aware funding corrections.
- Variants F and H largely fall outside Paper 1's risk framework as they lack terminal collapse, though they introduce unique reflexivity and manipulation risks.
Structural Findings:
- Conditional Denominator Instability: A candidate non-portability proposition is identified where the conditional underlying becomes ill-defined and unhedgeable as the conditioning event's probability approaches zero, distinct from terminal collapse.
- Spread Resolution Risk: Event spreads require a three-channel decomposition of risk: first-leg execution, residual margin, and second-leg terminal collapse.
- Basket Margin Aggregation: Multi-leg baskets require jump-aware margin aggregation that is correlation-dependent under simultaneous resolution.
- Reflexivity: Variants F and H introduce reflexive feedback loops where trading on the derivative alters the underlying market dynamics, invalidating standard counterfactual replay methods.
Evaluability Framework: The paper establishes criteria for empirical evaluability, distinguishing between variants fully evaluable on existing PMXT v2 data (Variant A), those conditionally evaluable (Variants B, C, D), those requiring multi-week data (Variant G), and those not evaluable via counterfactual replay due to reflexive feedback (Variants F, H).

Results and Limitations
The paper does not present empirical results for the new variants, as it is theoretical in nature. Its "results" are the structural definitions and inheritance maps themselves.

Limitations: The taxonomy is not exhaustive; combinations of variants (e.g., a rolling cross-platform spread) are not treated as separate cases. No specific variant is claimed to be deployable in current market conditions. The paper explicitly states that Paper 1's framework has documented design tensions (e.g., halt-vs-margin scope distinctions) that are inherited by these variants, meaning the framework is not empirically validated as a deployable specification for any variant beyond the single-market case.
Scope: The analysis is restricted to single-platform (Polymarket) constituents. Cross-platform variants are identified as requiring additional infrastructure and are out of scope.

Significance
The paper's significance lies in providing the "formal scaffolding" and "design vocabulary" necessary for future research and engineering on event-linked perpetuals. By distinguishing variants whose surface features may appear similar but whose risk-engineering requirements differ structurally, the taxonomy prevents the conflation of distinct instrument classes. It serves as the connecting tissue for the broader four-paper research programme:

It provides the manipulation surfaces that serve as inputs for Paper 3 (manipulation theory and regulation).
It defines the evaluability boundaries and microstructure phenomena that Paper 4 (supply-side microstructure) will investigate.
It clarifies which components of the Paper 1 framework are robust and which require modification, guiding the development of deployable specifications.

Ultimately, the paper does not advocate for the deployment of any specific variant but establishes the structural distinctions required to make informed deployment decisions and to conduct subsequent research on manipulation, pricing, and microstructure.