讲座题目：The rough Hawkes Heston stochastic volatility model

讲座时间：2024年4月24日（星期三）下午14:00-15:30

讲座地点：线下，博学925

主 讲 人：

Prof. Simone Scotti

意大利比萨大学经济与管理系副教授

主讲人简介：

Simone Scotti was born in Italy and graduated from Ecole Normale Superieure (Paris, France) with a bachelor in physics and a master in applied mathematics in 2005. He defended his PhD at Scuola Normale Superiore in 2009 under the direction of Nicolas Bouleau. He held a temporary post-doc at Ecole Polytechnique Federale de Lausanne and then worked as assistant professor at Université Paris VII. He obtained his habilitation as full professor in 2017. In 2022 he joined the University of Pisa as associate professor after an international selection. He currently works on applied probability and control theory with applications in economics and finance. His work has been published in journals such as the European Journal of Operational Research, Annals of Operations Research, Mathematical Finance, Finance and Stochastics, SIAM Journal on Financial Mathematics, Energy Economics, and many others.

讲座内容简介：

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to capture the joint evolution of the S&P 500 and VIX. (This is a joint work with Alessandro Bondi at Institute Polytechnique de Paris in France and Sergio Pulido at Université Paris-Saclay in France.)