A Study On The Volatility Of Stock Markets In China Based On Beyesian Heavy-tailed Stochastic Volatility Models With Jumps

Volatility is one of the most important features in financial markets, which is the core variable of the capital asset pricing, risk management and portfolio theory. Typically, there are mainly two categories used to describe the volatility of financial time series. One category is ARCH(autoregressive conditional heteroscedasticity) model, in which the conditional variance is the linear form of the past obervations and the squared error. The other is stochastic volatility model, in which the variance is decided by an unobserved stochastic process, which is different from ARCH, so stochastic volatility is considered more suitable for the empirical study of the financal sector. However, stochastic volatility model has its own flaws, namely which cannnot describe the unexpected financial fluctuations features which is called jump features, and this type of volatility is real in practice. Therefore, this paper proposes the Bayesian heavy-tailed stochastic volatility models with jumps to describe the jumps characteristics in financial time series.First, in terms of the structural ananlysis of the heavy-tailed stochastic volatility model with jumps, their state space transition and bayesian inference on the parameters of the models, we construct a Markov Chain Monte Carlo algorithm to estimate parameters, and utilize Kalman filters and Gaussian simulation smoother to analyze the latent volatility implied in models. And then we use the Gaussian kernel density estimation method to estimate the posterior density function values of the models’ parameters and accordingly design the kernel density algorithm to calculate the marginal likelihood function of the heavy-tailed stochastic volatility model with jumps, so as to solve the Bayes factor computation. Finally, we select the Shanghai Composite Index as the object of study, to analyze the characteristics of the volatility of the stock markets of China, and compare with the characteristics of the volatility of the stock markets of the U.S.. At the same time, the use of Bayes factors to conduct a comparative analysis on the fat-tail stochastic volatility model with jumps, heavy-tailed stochastic volatility model and the standard stochastic volatility model.The results show that the characteristics of continuity and jumps are significant both in the stock markets in China and the U.S., and the jumps in frequency and volatility levels of the stock market in China are higher than those of the U.S., but the scales of the jumps are smaller than those of the U.S.. The heavy-tailed stochastic volatility model with jumps is superior to the heavy-tailed stochastic volatility model and the standard stochastic volatility model in depicting the character of volatility, while the heavy-tailed stochastic volatility model is superior to the standard stochastiv volatility model.