The Application Of Non-symmetry Model In The Research Of Financial Markets Returns And Volatility

In recent years, the research of volatility has great significance in the financial field.The volatility of stock market has many features:time-varying, long memory, leverage effect and so on.This paper studies the volatility feedback effects and leverage of our stock market.The research of volatility of financial markets experienced rapid development and change, but the domestic research in this area is still relatively small.Especially for continuous-time volatility model, there is a huge space for development, especially for the parameter estimation of continuous-time volatility model.Many learn has been committed to the research of stochastic volatility models and made many parameter estimation methods, such as the method of moment estimation, maximum likelihood estimation, MCMC estimation and so on.This paper begains from the development of stochastic volatility model, use the theory of stochastic differential equations to study the relationship of the financial market returns and volatility. Use Milstein method discrete continuous stochastic volatility model, use MCMC methods to estimate the parameters of continuous stochastic volatility model. Analysis volatility feedback effect and the leverage effect of our stock market.After the introduction of this paper, first introduces the theory of stochastic differential equations, including the nature of Brown motion,Ito formula and the solutions of stochastic differential equations. Then introduces the theoretical model of the relationship between return and volatility, including volatility feedback effect model, leverage effect model and volatility forecasting bias model,and use the Milstein method discrete continuous stochastic volatility model, then use MCMC methods to estimate parameter with our stock market data.Finally, analysis and summarize volatility feedback effect and the leverage effect of our stock market.In this paper, MCMC method used in parameter estimation of continuous time volatility model,make a study of volatility feedback effect and leverage effect of our stock market,in the financial field has an important practical significance.