  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 tigger endogenous jump cascades in
asset returns and stock price volatility.
