“…Many studies provide empirical evidence that the VIX and its derivatives are sensitive to jump risk (e.g., Dew‐Becker et al, 2017; Duan & Yeh, 2010; Eraker & Wu, 2017; Lin, 2007; Mencía & Sentana, 2013; Park, 2016). Recent empirical evidence indicates that the Hawkes jump model (Hawkes, 1971) can capture jump propagation risks in the market and is essential for asset pricing (e.g., Aït‐Sahalia et al, 2015; Boswijk et al, 2015; Du & Luo, 2019; Liu & Zhu, 2019). We depart from these studies and seek to answer whether embedding jump propagation risks in the return dynamics can improve the fit performance of a model and what role the Hawkes jump model plays in the representation of the VIX term structure under different circumstances.…”