THE MICROSTRUCTURE OF STOCHASTIC VOLATILITY MODELS WITH SELF-EXCITING JUMP DYNAMICS

• 成果类型: Article
• 署名作者: Horst, Ulrich; Xu, Wei
• 署名单位: Humboldt University of Berlin; Humboldt University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1796
• 发表日期: 2022
• 页码: 4568-4610
• 关键词: limit-theorems; hawkes processes; price; distributions; diffusion; implicit; BEHAVIOR; SPECTRA; options; IMPACT

摘要

We provide a general probabilistic framework within which we estab-lish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Vari-ous well-studied stochastic volatility models with and without self-exciting price/volatility co-jumps are obtained as special cases under different scaling regimes. We analyze the impact of external shocks on the market dynamics, especially their impact on jump cascades and show in a mathematically rig-orous manner that many small external shocks may trigger endogenous jump cascades in asset returns and stock price volatility.