Bayesian Analysis of Bitcoin Volatility Using Minute-by-Minute Data and Flexible Stochastic Volatility Models

Makoto Nakakita (), Tomoki Toyabe and Teruo Nakatsuma
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Makoto Nakakita: Center for Advanced Intelligence Project, RIKEN, Chuo 103-0027, Tokyo, Japan
Tomoki Toyabe: Faculty of Economics, Kanazawa Gakuin University, Kanazawa 920-1392, Ishikawa, Japan

Mathematics, 2025, vol. 13, issue 16, 1-26

Abstract: This study analyzes the volatility of Bitcoin using stochastic volatility models fitted to one-minute transaction data for the BTC/USDT pair between 1 April 2023, and 31 March 2024. Bernstein polynomial terms were introduced to accommodate intraday and intraweek seasonality, and flexible return distributions were used to capture distributional characteristics. Seven return distributions—normal, Student- t , skew- t , Laplace, asymmetric Laplace (AL), variance gamma, and skew variance gamma—were considered. We further incorporated explanatory variables derived from the trading volume and price changes to assess the effects of order flow. Our results reveal structural market changes, including a clear regime shift around October 2023, when the asymmetric Laplace distribution became the dominant model. Regression coefficients suggest a weakening of the volume–volatility relationship after September and the presence of non-persistent leverage effects. These findings highlight the need for flexible, distribution-aware modeling in 24/7 digital asset markets, with implications for market monitoring, volatility forecasting, and crypto risk management.

Keywords: Bitcoin; cryptocurrency; Bayesian analysis; stochastic volatility; Markov chain Monte Carlo; ancillarity–sufficiency interweaving strategy; seasonality; high-frequency trading (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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