Paper: arXiv 2610.22839

Authors: Donghwa Seo, Doohwi Cha, Seunghan Son, Juyeong Lee, Minsuk Sung, Minjae Lee

Abstract

Crypto venues increasingly list perpetual futures on equities and other real-world assets (RWAs), which trade continuously yet reference dividend-paying stocks: a long equity perpetual marked to the ex-dividend cash price bears the ex-dividend drop without receiving the dividend. We ask whether the premium-index funding architecture these venues run – funding set from the contemporaneous basis $e_t=P_t-S_t$ rather than a carry target – can replicate shareholder cash flows for traders entering and exiting at arbitrary times. It cannot. Funding serves two roles that coincide for non-dividend crypto assets but split apart for equities: basis control and settlement. We give the fair-funding identity, cast timing fairness as an optimal-stopping condition, and characterize when the basis is a sufficient statistic for the fair target. The decisive obstruction is measure-theoretic: a predictable dividend is an atom, and no absolutely continuous funding path can replicate an atom over holding intervals even in the weak limit, so fairness must match the atom with an atom – an event credit. Exchange-native data confirm this: at each covered ex-date one venue posts a discrete funding atom equal to $-D/(\mathrm{Mark}-D)$ while a standard premium-index venue posts none, transferring the dividend across venues – from native funding alone, with no external spot.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel and critical analysis of funding mechanisms in crypto equity perpetuals, backed by a strong theoretical framework and empirical validation using exchange-native data. The mathematical treatment of fair funding and dividend atoms is sophisticated, and the empirical findings directly support the theoretical claims, highlighting a significant market design flaw.

Research Flowchart

  flowchart TD
    A[Research Goal: Can premium-index funding replicate shareholder cash flows for RWA perpetuals?] --> B{Methodology: Fair-Funding Identity & Optimal-Stopping}
    B --> C{Data/Inputs: Exchange-native data, Ex-dividend dates, Premium-index funding architecture}
    C --> D[Computational Processes: Analyze funding paths, Identify predictable dividends as atoms, Compare funding mechanisms]
    D --> E[Key Finding: Basis-only funding is NOT dividend fair; Cannot replicate atoms]
    E --> F[Outcome 1: Funding serves split roles (basis control & settlement) for equities]
    E --> G[Outcome 2: Fair funding requires matching dividend atom with an event credit (e.g., -D/(Mark-D) discrete funding atom)]