Jump Behavior Of The Stock Market-via The Time Varying Jump-Diffusion Model

As an emerging stock market, Chinese stock market has been frequently intervened by the Central government. In order to learn the abnormal return of the Chinese stock market, we consider the Poisson jump diffusion process trying to capture the jump behaviors of the Chinese and American stock market. Volatility clustering is a well-known financial stylized fact, this phenomenon also takes place in the jump behavior, that is to say, there exists jump clustering. In order to study the jump clustering phenomenon, this paper applies the auto regression model of the jump intensity set up by Maheu (2002). A vast number of literatures have show that not only shall we consider the jump process in the return process, we also must take into account of the jump process in the volatility process. Therefore ,when using the EGARCH model to describe the volatility , I consider the volatility of the normal innovations is a not only the function of the past normal innovation, but also affected by the past jump innovation.Empirical results show that there exists jump behavior both in the Chinese and American stock market. The stylized fact of jump clustering is obvious in both market, the volatility process is truly affected by the jump process. However, there are some differences between the two markets. The results show that the Chinese stock market is much more fluctuant than the American stock market. The average proportion of the jump variance is 30.54 % for SCI, while the proportion of DJIA's is only 9.38 %. All these results are in accordance with the different situations of the two markets.I apply the Hong and Li (2005) test to do model specification test. I find that EGARCH-GED model can not be rejected by Hong and Li test in sample for the SCI(Shanghai Composite Index), while all the other models are rejected ,which shows that EGARCH-GED model outperforms the different kinds of models considering poisson jump diffusion process when used to describe the distribution of the index return. I also find that performances of all these models are similar when used to describe the distribution of DJIA (Dow Jones Industrial Average).