Dynamic Financial Volatility Model Based On Non-normal Distribution

The risk measure and assessment is one of the most important contents of risk management. Variance is the best measurement under the condition that the return distribution of risk asset is normal. However, many researches have the conclusion that the return distribution has fat-tails and skewness. This paper studies financial volatility on condition of non-normal distributions and includes five aspects:1. An empirical test and theory explanation of the non-normal distributional characters of returns. There are two reasons of price abnormality, the subjective is the market factors and the objective is the psychology factors of investors. So, at first, an empirical test of the non-normal distributional characters of returns is to study. Then we will explain the reasons of the non-normal distributional characters of returns through Financial Market Microstructure and Behavior Financial Theory.2. A model of conditional Volatility and VaR of high frequency extreme value based on generalized extreme value distribution. Considering the factors of anticipation and volatility, to catch the character of return series in extreme condition and improve VaR precision, a model of conditional extreme value VaR is established. The time-varying parameters of conditional generalized extreme value distribution is estimated using intelligence optimization algorithm, calculating the diversified extreme value VaR at the different block and checking the results by invoking Kupiec-LR and dynamic quantile test. The analysis on models and VaR shows that conditional generalized extreme value distribution is better fitted with the feature of return series in extreme condition. Comparing our model with McNeil's, Kupiec-LR and dynamic quantile test of conditional extreme value VaR using high frequency return perform well,which has the implication that our model can catch the risk character of Chinese stock markets and improve estimation in extreme condition..3. A model of dynamic fitting the heavy-tailed distribution based on L-moments. To solve moment estimation problems in heavy-tailed distribution which do not possess set of finite central moments, introducing the theory of L-moments which is developed in hydrology. Considering the factors of anticipation and volatility, fitting the tail with Generalized Pareto Distribution using high frequency excess return in the static and dynamic condition, checking the results by invoking Kupiec-LR and dynamic quantile test. The analysis on models and VaR shows that problems of moment estimation in heavy-tailed distribution can be solved with L-moments. Generalized Pareto Distribution is better fitted with the feature of return series in extreme condition, which has the implication that our model can catch the dynamic character of return series in extreme condition.4. A model of multivariate conditional Variance skewness kurtosis. Considering the factors of anticipation and volatility, to measure the dynamic character of higher moments risk and investigate the impacts of the risk on multi-financia1 markets or assets, a model of multivariate conditional higher order moments, which can solve the problem of'dimension disaster', is proposed with the determination of the formulas between moments and co-moments. The time-varying parameters of higher order moments are estimated using Dynamic Conditional Correlation, Autoregressive conditional density and intelligence optimization algorithm on the distribution. The analysis on models shows that model of multivariate conditional higher order moments is better fitted with the feature of higher order moments of return series. Comparing our model with others, the model perform well in solving the problem of'dimension disaster', which has the implication that our model can catch the risk character of Chinese multi-markets and improve estimation in multivariate conditional higher order moments.5. Portfolio with higher moments considering parameter uncertainty. Given the limitation of traditional portfolio theory, the model of portfolio with higher moments with skew-t distributions, and a method for optimal portfolio selection using a Bayesian decision theoretic are proposed. We employ the MCMC which estimated the parameters of skew-t distributions and the weights of portfolio. Our results suggest that it is important to incorporate higher order moments in portfolio selection. Further, it is very important that parameter uncertainty is to handle estimation error with expected utility.