The importance of jump clustering is widely recognized in the financial market. We use the Hawkes process to capture jump propagation risks and study their role in modeling the Volatility Index (VIX) term structure. Applying the joint estimation approach to the S&P 500 index and the VIX term structure, we find that incorporating jump propagation risks is important to reconcile the dynamics of joint data and to model the VIX term structure, especially when the market is highly volatile. The long‐term variance factor further improves the description of the VIX term structure for low and medium market volatility levels.

中文翻译：

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VIX期限结构：跳跃传播风险的作用

跳跃式聚类的重要性在金融市场中得到了广泛认可。我们使用霍克斯过程来捕获跳跃传播风险，并研究它们在波动性指数（VIX）期限结构建模中的作用。将联合估计方法应用于S＆P 500指数和VIX期限结构，我们发现合并跳跃传播风险对于调和联合数据的动态和建模VIX期限结构非常重要，尤其是在市场高度波动的情况下。长期方差因子进一步改善了针对中低市场波动水平的VIX期限结构的描述。