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.

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