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 Gaus s i an whit e noi s e s 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. The talk is based on joint work with Wei Xu.

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