The Study Of Volatility And Jump Of The Chinese Stock Market Based On The Jump-GARCH Model

Since the 1970s, with the deepening of the financial innovation and the continuous development of international capital markets, a large number of derivative financial instruments were created for investors'hedging and arbitrage transactions, which promoted the development of the capital market further. However, derivative financial instruments not only improved the capital market pricing mechanism, but also greatly increased the systemic risk of the capital market. After the U.S. subprime mortgage crisis, the financial crisis have expanded to the globe, making regulators and investors face to the market risks more seriously. In the risk management process, asset volatility is an important measure of risk indicators. Volatility can not be observed directly, so how to characterize the volatility with the quantitative methods became the focus of the domestic and foreign scholars.Engle's ARCH model in 1982 and Bollerslev's GARCH model in 1986 made the study of volatility to a new stage. Since then, the GARCH family models based on the ARCH model and GARCH model have been widely used in the field of volatility study. The GARCH family models can describe the characteristics of the assets'volatility well, but they can not explain some unusual fluctuations in asset prices, such as the "Black Monday" the U.S. stock market suffered inl987 and the U.S. stock market crash after the "9.11" incident. Such unusual fluctuations often reflect the jump in asset prices, and this jump often results in catastrophic loss of investors. So a large number of scholars strive to more accurately describe the asset price jumps and volatility by the Jump-GARCH model and the GARCH model. The empirical studies show that, the Jump-GARCH models can characterize the asset price volatility and jump features better.This paper selected four stocks as sample to study the volatility in China's stock market by non-homogeneous and non-symmetrical Jump-GARCH model. The Jump-GARCH model has complex structures and lots of parameters, so the traditional optimization algorithm for solving the likelihood function requires a lot of complex calculations and it's difficult to find the global optimal, which will make a lack of the accuracy of the parameter estimation. In order to overcome the shortcomings of traditional optimization algorithms, this paper uses the simulated annealing algorithm to optimize the likelihood function. Simulated annealing algorithm is an intelligent optimization algorithms based on the computer technology. Its programming is simple and it can find the global optimum. So this article uses simulated annealing algorithm in Java to estimate Jump-GARCH model parameter, which is one of the innovations.This paper analyses the volatility and jump features of the stocks based on the parameter estimation of the samples. First, the paper tests the various parameters in the jump process by the likelihood ratio test. The results show that:the sample stocks are jumping; the jumping are cluster, non-homogeneous and non-symmetry; different stocks'features are different in degree. Second, this paper studies the jumping probability of the four stocks in each time point. Third, this article divides the volatility of our stock into two parts:the smooth volatility and the jump volatility. The smooth volatility can be used to measure the systemic risk of the stock, and the jump volatility can be used to measure the non- systemic risk of the stock. So we can study the risk structure of each stock. Finally, we study the performance of different stocks after the sharply fell according to the mean of each stock jump, jump clustering, non-homogeneous, non-symmetry and the strength of the different risk structures. So that investors can grasp the timing of the sale to improve the investment income.The inadequacies of this article are as follow:First, we assume that residuals follow a normal distribution, but the asset return series are often subject to a thick-tailed distribution; second, this paper describes the number of jumps with the Poisson distribution, while the 0-1 distribution, negative binomial, etc. can also be used to describe the number of jumps; third, this paper describes the range of the jump by the normal distribution, but other distributions can also be used to measure the jump range. Therefore, the follow-up studies should primarily focus on these three points.