发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种融合恐惧与贪婪指数和学生t分布的部分观测马尔可夫过程模型，用于比特币波动率建模，在对数似然和滤波器稳定性上显著优于基准模型，验证了情绪信号和重尾噪声对捕捉加密货币市场波动与制度转换的有效性。
AI 中文摘要
加密货币市场表现出极端的价格波动和由情绪驱动的制度转换，传统波动率模型往往无法捕捉这些特征。为解决这一问题，我们开发了一个部分观测马尔可夫过程（POMP）模型，并增强了情绪和重尾分布。具体而言，我们扩展了Breto的框架，将恐惧与贪婪指数（FGI）作为外生回归变量纳入潜在波动率动态，并将高斯测量噪声替换为学生t分布。我们使用2020年1月至2025年4月的每日比特币收益和FGI数据，通过基于模拟的推断拟合模型。我们的方法在对数似然和滤波器稳定性方面显著优于三个基准模型。此外，我们的模型产生了与金融波动率已知特征一致的可解释参数。这些结果表明，纳入情绪信号和重尾噪声改善了加密货币市场中波动率和制度转换的建模。
英文摘要
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.
