The Alpha-Heston stochastic volatility model

We introduce an affine extension of the Heston model, called the alpha-Heston model, where the instantaneous variance process contains a jump part driven by alpha-stable processes. 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.