Abstract: We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by α-stable processes with α ∈ (1, 2). In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. In particular, we show that the behavior of stock implied volatility is the sharpest coherent with theoretical bounds at extreme strikes independently of the value of α ∈ (1, 2). As far as variance options are concerned, VIX^2-implied volatility is characterized by an upward-sloping behavior and the slope is growing when α decreases. Furthermore, we examine the jump clustering phenomenon observed on the variance market and provide a decomposition formula which allows to analyse the cluster processes.

Bio: Ying Jiao is a professor of applied mathematics at Institute of Financial and Actuarial Sciences of University of Lyon 1. Her research domains are financial mathematics and applied probability including risk modelling and management in finance and insurance, stochastic control and optimization etc.