| Volatility is the key variables of investment portfolio,the capital asset pricing and risk management theory,and is a core issue of research on the financial markets.Because of some disadvantage of the existing financial asset prices and its volatility model,they are difficult to fit the movement behavior of financial markets which have emergencies,and with the strengthening of the complexity of the model,parameter estimation brings a lot of restrictions to the practical application of the model.Therefore,it is highly significant to seek suitable models and suitable methods for studying the volatility of financial assets.At present,there are mainly two models used to describe the volatility of financial time series.One is the autoregressive conditional heteroscedasticity model(ARCH)and the other is the stochastic volatility model(SV).But the difference is that the variance in the stochastic volatility model is determined by an unobservable random process,which can better fit the characteristics of the spikes,thick tails,and long memory of financial time series,and is more suitable for practical research in the financial field.In addition,due to the impact of emergencies,financial time series also have the characteristics of jumping movements,while the basic random fluctuation model cannot characterize jumping movements in the yield sequence.Therefore,in this paper,the jumping behavior is combined with the SV model as a random event to construct the SV-Jump model,which can not only solve the spikes and thick tails of asset timing,but also the jumping effect of timing.However,the SV-Jump model belongs to a high-dimensional complex nonlinear model,and the traditional gradient algorithm will cause great inconvenience when estimating model parameters.Moreover,in the stochastic wave model,the joint posterior distribution is high-dimensional,the state variable volatility is implicit and unobservable,and the posterior distribution of some parameters is not normal distribution,gamma distribution and other standard distribution densities,which is complicated The form of posterior distribution density makes it difficult to use some classical estimation methods to estimate it,so this paper adopts Markov chain Monte Carlo(MCMC)simulation method to solve the parameter estimation problem.Because the Bayesian inference method can effectively solve the problem of estimating the high-dimensional distribution parameters in the model,this paper establishes the SV-Jump model and attempts to study the fluctuation of the Shanghai and Shenzhen 300 stock indexes based on the MCMC method.First,the Bayesian method is used to infer the posterior distribution of the parameters in the SV-Jump model;Secondly,Monte Carlo numerical simulation is performed on the SV-Jump model,and MCMC method is used to estimate the parameters in the model.According to the MC error,BGR ratio,and autocorrelation plot results,the MCMC method is used to determine the parameters and status of the SV-Jump model.The effect of the variable is better;Finally,using the Shanghai and Shenzhen 300 Index as a representative,the closing price data of a total of 2431 trading days from January 4,2010 to December 31,2019 were selected as sample data.An empirical study of the SV-Jump model was conducted.The results show that The model can better analyze the volatility and jump of return.At the same time,the models were compared and analyzed according to the DIC criterion,and the results showed that the SV-Jump model fits the data best.In the application part of the model,the quantile regression method is used to calculate the value-at-risk(Va R)of the four models: GARCH(1,1)-t model,SV-N model,SV-T model and SV-Jump model.The SV-Jump model has the best effect on risk measurement.In summary,the MCMC method is reliable and effective for parameter estimation of the SV-Jump model.It also shows that the model and method can provide a certain value reference for financial investment and risk control. |
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