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

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.

💡 Research Summary

The paper “Cryptocurrencies and Interest Rates: Inferring Yield Curves in a Bondless Market” tackles the fundamental problem of constructing term‑structure curves for digital assets in an environment where traditional bond markets are virtually absent. After a thorough historical review of interest‑rate practices from ancient Mesopotamia to modern Europe, the authors argue that the lack of fixed‑rate debt instruments does not preclude the inference of a yield curve; rather, it forces analysts to rely on alternative market data.

The core contribution is a methodological framework that extracts risk‑neutral interest rates from the highly liquid cryptocurrency derivatives market—specifically perpetual futures, dated futures, and options—supplemented by on‑chain lending rates from DeFi protocols. The process proceeds in three stages:

1. Short‑term rate estimation – The funding rate of perpetual futures is interpreted as an implicit overnight rate. By aggregating funding data across major exchanges (Binance, Bybit, Deribit, etc.) the authors obtain a reliable 1‑day to 1‑week rate series.

2. Bootstrapping medium‑ and long‑term rates – Prices of dated futures are inverted under the risk‑neutral assumption to recover the expected spot price at each maturity. From these expectations, the corresponding continuously‑compounded forward rates are computed, yielding a discrete set of term points (1 month, 3 months, 6 months, 12 months, etc.).

3. Smoothing and model calibration – The discrete forward rates are fitted with B‑splines (or natural splines) while penalizing the second derivative to avoid over‑fitting. The resulting smooth curve serves as the input for calibrating stochastic interest‑rate models such as Vasicek, Hull‑White, and CIR via least‑squares minimization. This yields a full risk‑neutral short‑rate process that can be used for discounting cash flows, pricing exotic derivatives, and performing scenario analysis.

Empirically, the framework is applied to Bitcoin (BTC) and Ethereum (ETH) using data from 2023‑2024. The derived yield curves are compared against DeFi lending rates (Aave, Compound) and traditional bond‑derived curves (where available). The authors find that derivative‑based rates exhibit lower volatility and a more coherent term structure than raw DeFi rates, which are often noisy and heavily influenced by platform‑specific liquidity. Moreover, when the calibrated Hull‑White model is used to price observed options, the average absolute pricing error stays below 2.3 %, confirming the internal consistency of the inferred curve.

The paper also discusses several limitations. In markets with thin derivative liquidity—particularly for smaller altcoins—the bootstrapping step can become unstable, leading to noisy forward rates. Funding rates, while useful, are mechanically designed to equalize perpetual and spot markets; they can be distorted during periods of extreme leverage or rapid spot price swings. The choice of spline order, smoothing penalty, and weighting across exchanges introduces a degree of subjectivity that may affect the final curve. Finally, the current approach does not explicitly model credit risk or default probability, which are inherent to traditional sovereign or corporate yield curves.

To address these gaps, the authors propose future research directions: integrating on‑chain loan and staking yields to capture credit‑related spreads, employing Bayesian filtering or machine‑learning smoothing to reduce parameter sensitivity, and developing adaptive calibration schemes that react to regulatory or market‑structure changes in real time. Cross‑asset arbitrage strategies that exploit discrepancies between derivative‑implied curves and DeFi lending rates are also suggested as a practical application.

In conclusion, the study provides a novel, data‑driven methodology for constructing cryptocurrency yield curves without relying on bond issuance. By leveraging the depth of the derivatives market, it offers a viable alternative for discounting, risk management, and pricing in the nascent digital‑asset ecosystem, while highlighting the need for ongoing refinement to handle liquidity shocks, credit considerations, and the evolving regulatory landscape.