The alpha-Heston stochastic volatility model

We  introduce  an  affine  extension  of  Heston  model,  called  theα-Heston  model,  wherethe instantaneous variance process contains a jump part driven byα-stable processes with α∈(1,2].  In this framework, we examine the implied volatility and its asymptotic behaviorsfor 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 other "children jumps" characterizing the contagion impact.