Paper: arXiv 2212.06888

Authors: Songrun He, Asaf Manela, Omri Ross, Victor von Wachter

Abstract

Perpetual futures are the most popular cryptocurrency derivatives. Perpetuals offer leveraged exposure to their underlying without rollover or direct ownership. Unlike fixed-maturity futures, perpetuals are not guaranteed to converge to the spot price. To minimize the gap between perpetual and spot prices, long investors periodically pay shorts a funding rate proportional to this difference. We derive no-arbitrage prices for perpetual futures in frictionless markets and bounds in markets with trading costs. Empirically, deviations from these prices in crypto are larger than in traditional currency markets, comove across currencies, and diminish over time. An implied arbitrage strategy yields high Sharpe ratios.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This foundational paper provides a rigorous mathematical framework for pricing perpetual futures while backing it up with solid empirical analysis of crypto market dynamics. The identification and backtesting of the implied arbitrage strategy demonstrates both theoretical depth and strong practical relevance.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive Perpetual Futures Pricing & Quantify Arbitrage] --> B[Input Data: Crypto & FX Spot/Futures Prices, Funding Rates]
    B --> C[Theoretical Modeling: Derive No-Arbitrage Bounds in Frictionless & Costly Markets]
    C --> D[Empirical Analysis: Measure Spot-Perpetual Deviations & Strategy Returns]
    D --> E[Finding 1: Price deviations are larger than FX but diminish over time]
    D --> F[Finding 2: Implied arbitrage strategy yields high Sharpe ratios]