Abstract: In this essay, large volatility mutually exciting effect between international crude oil market and Chinese stock market are discussed under the circumstances that the two markets have shown greater synchronicity in terms of volatile events over the past ten years. For example, on August 24, 2015, the global stock market crashed and fell into a precipitous spiral, with the CSI300 index plunging 8.75%. Crude oil prices were hit hard by market concerns that a slower recovery in crude oil demand would exacerbate the global supply glut. Brent crude oil futures plunged 6.56% from the previous trading day. It is of great significance to research the propagation characteristics of large fluctuations between international crude oil market and Chinese stock market from the perspectives of stock market construction, asset allocation and risk prevention. There are some defects in the three traditional research methods on the volatility spill-over effect: Multivariate GARCH Model, Extreme Value Theory and Copula. Hawkes process is a path-dependent random point process, whose core idea is that the occurrence of any event will increase the frequency of subsequent events, but this effect will decay in some form over time. So Hawkes process is a more compatible choice for modeling large volatility mutually exciting effect. The 2-dimensional marked Hawkes process is used to model the self- and mutual-excitation of large fluctuations of Brent crude oil futures and CSI300 index from 2007 to August 15, 2019, after the adjustment of statutory holidays and bilateral exchange rate. It is found that: (1) The Hawkes process can properly describe the single market continuation and cross-market contagion between international crude oil market and Chinese stock market, and capture the aggregation, persistence and spillover of asset returns in time and space. (2) There is a strong self-excitation in both crude oil market and Chinese stock market, respectively. (3) The mutual-exciting effect between the two markets is statistically significant, but weaker in actual impact than the self-excitation.

Key words: Hawkes process; extreme value theory; large fluctuations; mutually exciting effect