🤖 AI Summary
Existing research on event-linked perpetual contracts is confined to binary setups within a single market, lacking a systematic taxonomy and a unified risk modeling framework. This work proposes the first formal classification system, structured along four orthogonal design axes and encompassing seven variant types: conditional probability, spread-based, weighted basket, volatility/entropy-linked, liquidity-adjusted, rolling-structure, and unfunded settlement-free contracts. For each type, we rigorously define payoff structures, constraints, risk inheritance mappings, and microstructural mechanisms. Leveraging geometric insights from stochastic processes and a multi-period, jump-aware margining design, we uncover fundamental differences across variants in risk transmission, settlement logic, and temporal structure. Key challenges—such as denominator instability in conditional variants and a three-channel risk decomposition in spread-based contracts—are identified. Finally, we establish evaluability criteria based on PMXT v2 and constructible time-series methodologies to lay the theoretical groundwork for future empirical analysis.
📝 Abstract
Paper 1 of this research programme develops a resolution-aware risk-design framework for the simplest event-linked perpetual: a contract whose underlying tracks a single binary prediction-market probability through resolution. The instrument class is broader. Variants span conditional probabilities P(A|B), spreads p^A - p^B, weighted baskets sum w_i p^(i), derivatives on variance or entropy of the probability process, contracts on liquidity itself, perpetual-on-expiring-event roll structures, and funding-only derivatives with no settlement. Each variant inherits some framework components from the single-market binary case and requires its own design adaptations. This paper develops a formal taxonomy of seven pure-form canonical variants beyond the probability-index perpetual of Paper 1, organised along four orthogonal design axes: underlying geometry, temporal structure, settlement structure, and venue composition. The list is not exhaustive; combinations are not treated separately. For each variant we provide a precise payoff definition; an inheritance map identifying which Paper 1 components carry over, are modified, or fail; variant-specific design constraints; microstructure properties; empirical evaluability on the PMXT v2 archive; and limitations. Notable findings: the conditional variant admits a candidate non-portability proposition (denominator instability as the conditioning event becomes improbable); the spread variant requires a three-channel decomposition of resolution risk; the volatility/entropy variant avoids random binary terminal-collapse but introduces estimator-convention and entropy-decay issues; the basket variant requires multi-period jump-aware margin whose aggregation is correlation-dependent. The paper is theoretical primarily; it specifies how demonstrative time series can be constructed and provides evaluability criteria to guide future work.