学术讲座：The Alpha-Heston Stochastic Volatility Model

金融学院SBF论坛2019年第11讲

讲座题目：The Alpha-Heston Stochastic Volatility Model

时间：2019年5月6日（周一）12:20-13:30

地点：博学楼925

主讲人：焦莹

主讲人简介：

焦莹教授是里昂第一大学金融与精算科学研究所（Institute of Financial and Actuarial Sciences of University of Lyon 1）应用数学教授。她的研究兴趣包括金融数学和应用概率，涵盖金融和保险领域的风险模型、随机控制和优化等。

讲座内容简介：

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, VIX2-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.

本文对Hestion模型进行了仿射扩展，其瞬时方差过程包含一个由α ∈ (1, 2]的α-稳定过程驱动的跳跃。在这个框架下，本文检验了资产和方差期权的隐含波动率及其渐进性。特别的是，本文发现股票隐含波动率的行为与极端冲击下的理论边界相一致，而与α ∈ (1, 2)的取值无关。当考虑了方差期权时，VIX2隐含波动性表现出向上倾斜的特征，当α减小时，斜率增加。此外，本文检验了方差的跳跃聚集现象，并给出了可以用来分析聚类行为的分解方差。