Financial Volatility Models And Applications Based On Mixture Of Normal Approximation And Filtering Technology

In Financial random time series of stock options,spot crude oil prices,and gold prices,the risk management of financial asset price is increasingly important.Especially the financial crisis in 2008,the recent stock market fluctuation and crude oil prices plummeted,have highlighted the importance of the measurement of financial asset price volatility.Stochastic volatility(SV)model was proposed with history of almost three decades,it’s still in the ascendant with numerous studies in financial volatility modeling.And the SV model also is effective alternative and upgrade of the Generalized Autoregressive Conditional Heteroskedasticity(GARCH)model simultaneously.The SV model can be better to describe the typical feature of financial markets,such as volatility clustering,persistence and fat tail phenomenon.However,due to the introduction of nonlinear structure and the potential stochastic diffusion process in the SV model,the difficulty of the parameter estimation and the sample prediction is greatly increased.Fortunately,the SV model will be converted a non-Gaussian linear state space model without loss of any information in linearization.But the linearization process of SV model has brought the left-skewness and long-tailed.Based on principle of mixed Gaussian approximation,this paper use a finite mixture-of-normal to approximate the smooth non Gaussian distribution.So we can construct the SV models based on state space models with mixture-of-Gauss.For the parameters in such mixed Gaussian state space model to be estimated,we propose to the two step algorithm that combine Markov chain Monte Carlo(MCMC)simulation method and simulated EM algorithm.Compared with the existing methods,the mixed Gaussian approximation error significantly cut back.Further,in order to obtain the prediction of model’s out of samples,we introduce approximated filter(AMF)algorithm developed from standard Kalman filter algorithm.The AMF algorithm not only can be applied to the actual sequence longer time,the prediction accuracy is also close to exact filter.In the empirical study,the state space SV-N-MN model and SV-T-MN model are applied to study the time-varying volatility prediction respectively in the U.S.spot price of WTI crude oil market and Shanghai-Shenzhen stock market.The results show that the SV models based on state space models with mixture-of-Gauss is constructed in this paper,which has a significant improvement in the accuracy than the GARCHmodel,but also is more sensitive to the extreme risk.