A Research About Threshold Leverage Stochastic Volatility Model With Jump

The leverage effect,jump component and heavy-tailed errors in the time series of market asset returns are well-known and important.In order to fit some fea-tures in the time series of market asset returns better,this paper proposes thresh-old leverage stochastic volatility model with jump and heavy-tail,incorporating the jump component and student-t distribution to generalize the double threshold leverage stochastic volatility model proposed by Wu and Zhou.Rapid develop-ment in computer technology has made the financial transaction data visible at an ultimate limit level.Realized Volatility,as a proxy for the "true" volatility,can be constructed using the high-frequency data.This paper uses Realized Volatility to replace latent true volatility,and treats the volatility as an observed sequence.Due to the availability of the volatility time series,standard maximum likelihood estimation(MLE)is used in the parameter estimation process,which is easy than Bayesian method,and Monte Carlo simulation experiments are conducted.The proposed models show good performance according to the Monte Carlo results.In the section of empirical,the proposed models and methodology are applied to stock market index for China.Empirical results show that in different regimes,the volatility exhibit asymmetric behavior,and when the jump is significant,the model with jump proposed in this paper is better than the model without jump.