December 2022 The microstructure of stochastic volatility models with self-exciting jump dynamics
Ulrich Horst, Wei Xu
Author Affiliations +
Ann. Appl. Probab. 32(6): 4568-4610 (December 2022). DOI: 10.1214/22-AAP1796


We provide a general probabilistic framework within which we establish 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. Various 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 rigorous manner that many small external shocks may trigger endogenous jump cascades in asset returns and stock price volatility.

Funding Statement

Financial support from the Alexander-von-Humboldt-Foundation is gratefully acknowledged.


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Ulrich Horst. Wei Xu. "The microstructure of stochastic volatility models with self-exciting jump dynamics." Ann. Appl. Probab. 32 (6) 4568 - 4610, December 2022.


Received: 1 January 2020; Revised: 1 April 2021; Published: December 2022
First available in Project Euclid: 6 December 2022

Digital Object Identifier: 10.1214/22-AAP1796

Primary: 60F17 , 60G52 , 91G99

Keywords: affine model , branching process , Hawkes process , self-exciting jumps , stochastic volatility

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.32 • No. 6 • December 2022
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