Change-Point-Aware Stochastic Modeling of Cryptocurrency Volatility: Evidence from Bitcoin
TL;DR
It is suggested that allowing volatility to change at empirically identified points can provide a more useful stochastic representation of Bitcoin volatility than a single-regime GBM.
Abstract
Cryptocurrency prices often experience substantial changes in volatility over time, which may limit the usefulness of stochastic models based on a constant-volatility assumption. This study examines whether accounting for structural changes can improve the stochastic modeling of Bitcoin volatility. Daily Bitcoin prices from January 2020 to December 2025 are used to calculate log returns. A standard one-regime Geometric Brownian Motion (GBM) is first estimated as a benchmark, followed by a likelihood-based change-point analysis and a regime-dependent GBM. Model selection using the Bayesian Information Criterion favors the three-regime specification over the one- and two-regime alternatives. The estimated daily return volatility decreases across the training regimes, from 0.0446 to 0.0353 and then to 0.0248. The model is further evaluated using 2025 as an out-of-sample period. The change-point-aware GBM produces substantially lower forecasting errors than the standard GBM, with RMSE decreasing by 51.6% and MAE by 54.7%. These results suggest that allowing volatility to change at empirically identified points can provide a more useful stochastic representation of Bitcoin volatility than a single-regime GBM.