2025/04/29 by Hernán Larralde, Larralde, Hernán, Roberto Mota Navarro +1 · 1 voice
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Economics and business #Statistical Finance (q-fin.ST) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #q-fin.ST #stat.AP
paper · pdf · doi:10.48550/arxiv.2504.20488
openalex publication_date 2025/04/29 · arxiv published 2025/04/29 · arxiv updated 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S&P 500 index, Apple and Paramount stocks; and Bitcoin.