Modeling Study Of The Volatility Of Financial Data

Volatility of financial data has always been one of the hot topicsof Economics. It usually has two kinds of models to depict the volatilityof financial data: One is the ARCH-type models. It includesauto-regressive conditional heteroskedastic model(ARCH model)whichwas proposed by Engle in 1982 and generalized auto-regressiveconditional heteroskedastic model (GARCH model) which was proposedby Bollerslev in 1986, as well as expanded forms; the other is stochasticvolatility model and its expanded forms. It is very difficult to obtain theSV model's likelihood function, so it is difficult to estimate its parameters.In this paper, we use Bayesian method and regard the unknownparameters as random variables. First, we obtained the joint posteriordistribution of unknown parameters; then we regard the posterior mean asthe unknown parameters' estimate. As high dimension of the posteriordistribution, up to several thousand dimension, posterior mean'scalculation will be several thousand dimension's integration, so generalcompute method is difficult to solve it. Markov chain Monte Carlo(MCMC) method is a very effective method to solve the high-dimensionintegration problem. WinBUGS is the software that solves problemsbased on Bayesian analysis by MCMC method. The estimation of this paper's all parameters is completed by WinBUGS software throughprogramming. In this paper, we do comparative analysis of SV model andGARCH model by use of Shanghai Composite Index data. Compared byboth residual error and DIC criterion, we obtain that SV model is superiorto GARCH models. Then, we study the relationship between the stockprice volatility and turnover. To join the Shanghai stock market turnoverin various forms to SV model, we find that the stock price volatility andturnover are correlated positively and expected turnover is significantlydifferent from non-expected turnover to the price fluctuation's influence.Non-expected turnover has bigger influence than expected turnover to themarket impact, in other words, the market new information is the mainreason of price fluctuation.