Fear Moves Markets: Sentiment-Augmented POMP for Volatility Modeling of Bitcoin Returns
TL;DR
A partially observed Markov processes (POMP) model augmented with sentiment and heavy-tailed distributions is developed, extending Breto's framework by including the Fear and Greed Index as an exogenous regressor in the latent volatility dynamics and replacing Gaussian measurement noise with a Student's t distribution.
Abstract
Cryptocurrency markets exhibit extreme price swings and sentiment-driven regime shifts, which traditional volatility models often fail to capture. To address this, we develop a partially observed Markov processes (POMP) model augmented with sentiment and heavy-tailed distributions. Specifically, we extend Breto's framework by including the Fear and Greed Index (FGI) as an exogenous regressor in the latent volatility dynamics and replacing Gaussian measurement noise with a Student's t distribution. We fit the model via simulation-based inference using daily Bitcoin returns and FGI data from January 2020 to April 2025. Our approach significantly outperforms three benchmark models in log-likelihood and filter stability. Moreover, our model yields interpretable parameters consistent with known features of financial volatility. These results demonstrate that incorporating sentiment signals and heavy-tailed noise improves the modeling of volatility and regime shifts in cryptocurrency markets.