Comparison Of Stochastic Volatility Models Based On Bayesian Inference With Applications

In the stock market,the volatility of financial time series usually changes with time.In recent years,studying the characteristics of volatility in financial markets has become the focus of scholars.Using models to estimate volatility is one of the main methods for studying volatility.Therefore,to analyze the volatility of financial markets,the GARCH model and standard stochastic volatility(SV-N)model are widely used in the modeling of financial time series.However,the standard stochastic volatility model has potential volatility,which causes the likelihood function to become a complex high-dimensional integral.Therefore,many algorithms have been studied to solve this problem.This dissertation uses a specific prior distribution to construct an SV-N model using a Bayesian posterior distribution based on the MALA algorithm.The Bayesian estimates of the parameters obtained are compared with the estimated values of the stochvol software package and the Metropolis-Hastings algorithm to determine the accuracy of the model.Since the GARCH model also has disadvantages,its volatility is determined by the deterministic equation.Therefore,at the end of this dissertation,the Bayesian factor method is used to compare the GARCH(1,1)model with the standard stochastic volatility model on the simulation of financial time series.In this dissertation,the Shanghai Composite Index is the research object,and the daily closing price from December 31,2014 to December 31,2019 is selected as the research sample.The following conclusions are drawn: First,a descriptive statistical analysis of the daily returns of the Shanghai Composite Index is obtained,which shows the characteristics of volatility aggregation and peak and thick tails,indicating that this financial time series is suitable for establishing the SV-N model.Then,in terms of theoretical results,the posterior distribution of the MALA algorithm under a specific prior distribution condition is derived,and the Bayesian estimates of the parameters of this method are similar to those of the stochvol software package and the Metropolis-Hastings algorithm.Finally,according to the value of the Bayes Factor,it is concluded that the simulation effect of the SV-N model is superior to that of the GARCH(1,1) model.