<p>A novel fractal-based approach for the modelling and analysis of financial time series, in terms of both prices and log returns, is presented. In contrast to common approaches based on fractional Brownian motion or box-counting models, we employ a fractal interpolation-based methodology. Specifically, the proposed method models the time series with multiple recurrent fractal interpolation functions and then uses them to calculate a coefficient, which describes the complexity of the underlying time series. The employed methodology is designed to allow consistent calculations and thus the meaningful analysis and comparison of time series. In order to evaluate the proposed method, we use a dataset of eight major stock market indices (US, European and global) and eight dominant (in terms of market cap) cryptocurrencies for a 10-year testing period, namely from 1 January 2014 to 31 December 2023. The results show that the proposed fractal complexity coefficient of financial time series is a useful indicator being able to capture the dynamics of the relevant markets or assets.</p>