Cryptocurrencies and Interest Rates: Inferring Yield Curves in a Bondless Market

Paper: arXiv 2509.03964

Authors: Philippe Bergault, Sébastien Bieber, Olivier Guéant, Wenkai Zhang

Abstract

In traditional financial markets, yield curves are widely available for countries (and, by extension, currencies), financial institutions, and large corporates. These curves are used to calibrate stochastic interest rate models, discount future cash flows, and price financial products. Yield curves, however, can be readily computed only because of the current size and structure of bond markets. In cryptocurrency markets, where fixed-rate lending and bonds are almost nonexistent as of early 2025, the yield curve associated with each currency must be estimated by other means. In this paper, we show how mathematical tools can be used to construct yield curves for cryptocurrencies by leveraging data from the highly developed markets for cryptocurrency derivatives.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper addresses a highly original problem—constructing yield curves in cryptocurrency markets without a traditional bond market—by utilizing derivatives data. It combines strong mathematical framework design with deep historical context and practical market relevance, though reproducibility depends on access to specific crypto derivatives datasets.

Research Flowchart

  flowchart TD
    A["Research Goal: Infer Yield Curves in Bondless Crypto Markets"] --> B["Data Inputs: Crypto Derivatives Data (Futures, Options, Swaps)"]
    B --> C["Methodology: Extract Implied Interest Rates from Derivatives"]
    C --> D["Mathematical Modeling: Interpolate & Fit Term Structure"]
    D --> E["Outcome: Construct Crypto Yield Curves for Discounting & Pricing"]