The Empirical Research On Fluctuation Of SME Stock Index Based On The MCMC Method

With the rapid development of the financial market, the domestic financial products have also been introduced rapidly, the volume of business about exist products also increased significantly. Regardless of the market index to study, or on a single product, especially derivatives research, accurate analysis of its price fluctuations, is the key to identify risks and promote the healthy operation. Because China financial market started late, and the ratio of foreign mature financial markets, the impact of market volatility in many places have different factors, coupled with volatility in financial product pricing is an important content, and thus China domestic stock market volatility’s study is particularly important. SME index traded to the current time from the beginning is not long, but the transaction volume has increased in last years. In order to better understand the development of SMEs through the index, on the other hand something of national economic policies, or in order to better control the risk, the paper will study the volatility of SME in depth.Traditional GARCH model, the estimation of its parameters is based on the maximum likelihood by using the model theory that optimize the parameters are bound" by certain conditions, it is difficult to achieve precise parameters of the model, especially deviations, that it is difficult for optimal purposes.To better solve such a problem, this paper based on Bayesian Markov Monte Carlo (MCMC) approach to GARCH model parameter estimation, in order to better carry out the SME index volatility portrayed. Through a variety of statistical tests, the paper index returns for SME build a normal distribution based on GARCH (1,1) model. Using MCMC methods, the model parameter estimation and thus avoid the GARCH model restrictions on the parameter constraints, and solve the problem that can not be optimized. Compared to traditional BHHH algorithm and MCMC algorithm, MCMC method based on Bayesian theory can better estimate the parameters. This promote MCMC method,and also provides another idea about estimate the volatility parameterFirstly,we have a basic description about the time series volatility and introduce the basic characteristics for the characterization of ARMA model and GARCH model. Subsequently, the paper bring a brief description of mathematical formulas for the BHHH and MCMC algorithms. On this basis, the introduction of a relatively new evaluation model for the merits of the indicators to better prediction results were judged. We selected the domestic SME board for a long time the transaction data as a sample, respectively, a smooth, linear inspection of the basic characteristics of its establishment GARCH model, and using the above two methods to estimate analyzed to estimate the effect testing.At the same time, the paper also introduces the SV model as an analysis of the problem. SV model is another way to study the volatility problem, but because of the complexity of the calculations, it is not a popular GARCH models. With the rapid development of the computer, this is not a problem. SV model depicts the volatility index to be closer to reality, so in theory, should be better portrayed. MCMC-based approach by comparing the SV model and GARCH model, found in the SME index volatility portray aspects, SV model is better than the GARCH model characteristics.How to select a suitable method, a suitable model to characterize the index return volatility is very important. An accurate volatility, should carry out the pricing of financial assets well. Volatility is based asset pricing model, an accurate estimate of volatility is almost all financial assets and reasonable pricing of the premise. In China, more and more options continue to emerge, including a large number of embedded options, like financial products, regardless of its risk management or transaction, we need an accurate volatility, but at present, China has more macroscopic level management, for the relatively microscopic field, attention is not high. But combined with foreign countries above example shows microscopic field has been receiving increasing attention, in this context, this paper will be a combination of theory and practice, not only compared the estimated parameters of different methods, but also compared the different models. Index of SME rely on not only to identify the estimated model for SME index method, but also for future research on other issues provide some reference. Of course, this also has many shortcomings, such as the chosen model is not that the best model for the distribution of residuals is reasonable, and so future studies need to be resolved.