# Theory of Cryptocurrency Interest Rates

## TL;DR

This paper develops a term structure model for cryptocurrency interest rates, using zero short rate assumptions and local martingales to capture the unique features of digital currencies, with practical calibration to market data.

## Contribution

It introduces a novel zero short rate term structure model for cryptocurrencies, incorporating local martingales and providing explicit pricing formulas for bonds and derivatives.

## Key findings

- Model can be calibrated to initial yield curves
- Local martingales effectively model cryptocurrency pricing kernels
- Provides explicit formulas for crypto bond and derivative prices

## Abstract

A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can be calibrated to the initial yield curve and other market data. Our analysis suggests that strict local martingales can be used for modelling the pricing kernels associated with virtual currencies based on distributed ledger technologies.