The Alpha-Heston stochastic volatility model

We introduce an affine extension of the Heston model, called the α-Heston model, where the instantaneous variance process contains a jump part driven by α-stable processes with α ε (1,2].  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.