Paper: arXiv 2506.08573

Authors: Jaehyun Kim, Hyungbin Park

Abstract

In cryptocurrency markets, a key challenge for perpetual future issuers is maintaining alignment between the perpetual future price and target value. This study addresses this challenge by exploring the relationship between funding rates and perpetual future prices. Our results demonstrate that by appropriately designing funding rates, the perpetual future price can remain aligned with the target value. We develop replicating portfolios for perpetual futures, offering issuers an effective method to hedge their positions. Additionally, we provide path-dependent funding rates as a practical alternative and investigate the difference between the original and path-dependent funding rates. To achieve these results, our study employs path-dependent infinite-horizon BSDEs in conjunction with arbitrage pricing theory. Our main results are obtained by establishing the existence and uniqueness of solutions to these BSDEs and analyzing the large-time behavior of these solutions.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper offers a highly sophisticated mathematical treatment of funding rates in perpetual futures using path-dependent infinite-horizon BSDEs and arbitrage pricing theory. While it establishes groundbreaking theoretical results on existence, uniqueness, and replication for both tradable and non-tradable targets, it is entirely theoretical with no empirical data analysis or backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Align Perpetual Future Price with Target Value] --> B[Theory & Tools: Arbitrage Pricing Theory & Path-Dependent Infinite-Horizon BSDEs]
    B --> C[Methodology: Establish Existence & Uniqueness of BSDE Solutions]
    C --> D[Analysis: Analyze Large-Time Behavior of BSDE Solutions]
    D --> E[Outcome 1: Designed Funding Rates Maintain Price Alignment]
    D --> F[Outcome 2: Formulated Replicating Portfolios for Hedging]
    D --> G[Outcome 3: Provided Path-Dependent Funding Rates as Practical Alternative]