We introduce an affine extension of the Heston model, called the -Heston model, where the instantaneous variance process contains a jump part driven by -stable processes with . In this framework, we examine the implied volatility and its asymptotic behavior for both asset and VIX options. Furthermore, we study the jump clustering phenomenon observed on the market. We provide a jump cluster decomposition for the variance process where each cluster is induced by a “mother jump” representing a triggering shock followed by “secondary jumps” characterizing the contagion impact.

中文翻译：

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Alpha-Heston 随机波动率模型

我们引入了 Heston 模型的仿射扩展，称为-Heston 模型，其中瞬时方差过程包含由具有 的-stable 过程驱动的跳跃部分。在这个框架中，我们研究了资产和 VIX 期权的隐含波动率及其渐近行为。此外，我们研究了市场上观察到的跳跃聚类现象。我们为方差过程提供了跳跃聚类分解，其中每个聚类由代表触发冲击的“母跳跃”引起，然后是表征传染影响的“二次跳跃”。