The Alpha-Heston Stochastic Volatility Model

TL;DR

This paper introduces an affine extension of the Heston model incorporating alpha-stable jumps in variance, analyzing implied volatility behaviors and jump clustering phenomena in the variance market.

Contribution

It presents a novel affine Heston extension with alpha-stable jumps and provides analysis of implied volatility and jump clustering in variance options.

Findings

Implied volatility exhibits specific asymptotic behaviors under the new model.

Jump clustering phenomena are characterized and decomposed.

The model captures complex market behaviors related to variance jumps.

Abstract

We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $\alpha$-stable processes with $\alpha\in(1,2]$. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore, we examine the jump clustering phenomenon observed on the variance market and provide a jump cluster decomposition which allows to analyse the cluster processes.