Research On Volatility Modeling And Application Of CSGARCH Model Based On Tempered-Stable Distribution

Asset pricing and risk management are the core of today's financial engineering discipline research,and volatility is a factor that the two research cores must rely on.Constructing a dynamic time-varying model of volatility or applying a model to study the structure of financial asset volatility is an important research direction.The component autoregressive conditional heteroscedasticity?CSGARCH?model is extended to the autoregressive conditional heteroscedasticity?GARCH?model,which creatively separates the conditional variance into long-term components?Permanent?and short-term components?Transitory?.When applied to the study of financial time series,the Volatility is decomposed into short-term fluctuations and long-term fluctuations,so that short-term fluctuation effects and long-term fluctuation effects can be studied separately,providing a new perspective on volatility research.Like all GARCH family models,the original CSGARCH model's innovation sequence is usually assumed to follow a normal distribution.Subsequent studies have shown that this does not fit well with the thick-tail phenomenon of the financial asset rate of return sequence usually found in empirical data,leading to the model.The estimation is not efficient,and the tempered-stable distribution performs well in fitting the fluctuations of the yield series,has good stability,and is obviously better than other thick-tailed distributions such as the t-distribution and GED distribution.From the perspective of distribution selection,this paper introduces the tempered-stable distribution and solves the systematic integration of the tempered-stable distribution and the CSGARCH model.The Monte Carlo simulation method was used to compare the performance of the four distributions in the volatility fitting.The simulation results found that the CSGARCH model based on the tempered-stable distribution is always better than the CSGARCH model based on the 'traditional' distributions such as the normal distribution,the t distribution,and the GED distribution.Based on the simulation results,the daily volatility calculated based on the five-minute high-frequency data of the Shanghai Composite Index is used for empirical research.First fit the data with four models,and obtain the same results as the simulation process through the three indicators of Log likelihood,AIC,and BIC.Compare the four conditional volatility series generated by the fitting and find the height of the conditional volatility series.Similarly,turn to compare the performance of intra-sample and out-of-sample predictions of the four models.The prediction results were evaluated according to the RMSE,SE,Mean,Q₉5 indicators of the difference between the real volatility and the predicted volatility,and the CSGARCH-S model was confirmed to perform best.Finally,the CSGARCH model based on the tempered-stable distribution was applied to VaR calculations,and it was found that under the 97.5% confidence level,only the positive and negative bilateral violations of the VaR value generated by the CSGARCH-S model were less than 2.5%.Therefore,this paper believes that the CSGARCH model based on the tempered-stable distribution can be widely applied to economic and financial data modeling in general,and to optimize the level of risk management,especially when studying the long-term and short-term effects of univariate variables.