Financial Stochastic Volatility Extension Model Analysis And Applied Research

Recent years the stochastic volatility model develops very fast in our country, the researchers proposed lots of expanding models. But the quality of expanding models for simulating the finance time series does not have a conclusion. This article using Markov chain Monte Carlo algorithm procedure with Gibbs sampler to estimate the models's parameters and compare different SV models through the quality of simulate the characteristics of SZCI.This article first introduces the background of the financial stochastic volatility model, research status and the bayesian estimation method of the volatility model. Then, take SZCI and SSEC as illustrations, we do statistical analysis of the financial time series of our country. The study proves that Chinese stock market returns exist obvious leptokurtic phenomenon.The central work of the paper is from the chapter 3 to chapter 5, we use SZCI analysis the volatility of our stock market. Firstly, with the aid software WinBUGS, we use Markov chain Monte Carlo algorithm procedure with Gibbs sampler to estimate bayesian parameters of the standard SV model based on bayesian theorem. Secondly, we expand the standard SV model to two directions: Heavy-tail SV model, SVL-HS-N model and SVL-JAR-N model with leverage effect. We also establish MCMC algorithm procedure with Gibbs sampler to estimate parameters of different models with the aid software WinBUGS. Then, we construct SVL-HS-T model and SVL-JPR-T models based on heavy-tail and leverage effect. According to the simulation results of the characteristics of SZCI, we compare the two SV models. Finally, we expand the nonline SV model to nonline SV model with leverage effect.After the comparative analysis, we discover SZCI, behalf of the Chinese stock market, all display the property of strong volatility persistence, while volatility have the leptokurtic phenomenon; With leverage effect, SVL-JPR-N is better than SVL-HS-N in capture the asymmetric phenomenon of stock index respect; With heavy-tail and leverage effect, the SVL-HS-T model is better than SVL-JPR-T model in simulating effects respect; Using the nonlinear SVL model to simulate the SZCI, the estimation results show that the new information reaches SZCI with high frequency every day, the frequency has strong volatility.