摘要
风险管理的基础和核心是对风险的定量分析和评估。在风险资产的收益率服从正态分布的条件下,方差是最好的风险度量,而大量研究已经表明金融资产收益率是非正态的,是“厚尾”和“有偏”的。因此本文在非正态分布条件下讨论金融波动性建模研究。具体从以下几个方面进行了分析探讨:
1、金融收益序列非正态分布检验及理论解释。市场价格异常波动的原因,可以分为主观和客观两个方面,客观方面的原因来自市场本身,主要是制度因素;主观方面的原因来自投资者,主要是投资者的心理因素。因此,本章将首先介绍收益率非正态分布特征的检验方法,然后分别从市场微观结构理论角度和行为金融学角度讨论收益率分布尖峰厚尾特征以及偏度特征的形成原因,给出收益非正态分布的理论解释。
2、金融收益“厚尾”分布动态拟合(Ⅰ)——基于广义极值分布的自回归条件密度模型研究。在考虑当前预期和波动性条件下,为了有效地捕获极端条件下收益率时间序列动态特征,建立了基于高频数据的波动性模型和条件极值VaR模型。应用智能优化算法对条件极值分布的时变参数进行估计,考察了在不同样本容量分块下的条件极值VaR,并对VaR计算结果的精度进行了Kupiec-LR检验和动态分位数检验。研究结果表明,基于高频数据的条件极值分布较好的拟合了极端条件下的收益率特征,与McNeil提出的传统条件极值VaR相比,应用高频数据建立在条件广义极值分布基础上的条件极值VaR的Kupiec检验DQ检验值都较为理想,表明该模型能够捕捉到我国市场风险特征,提高极端情况下风险测度能力。
3、金融收益“厚尾”分布动态拟合(Ⅱ)——基于广义帕雷托自回归条件L-矩模型。为了解决厚尾分布不拥有完整的中心矩集合而无法进行矩估计的问题,在金融领域引入近年来在水文领域发展较为迅速的L-矩理论。在考虑当前预期和波动性条件下,基于L-矩理论分别考察了广义帕雷托分布对高频收益超额数的静态尾部拟合和动态尾部拟合,应用条件VaR以及Kupiec-LR检验对拟合的结果进行了检验。研究结果表明,L-矩理论可以很好的解决厚尾分布的矩估计问题,根据VaR以及Kupiec-LR检验表明,基于L-矩的广义帕雷托分布较好的拟合了极端条件下的收益率尾部,可以捕获极端条件下收益率时间序列动态特征。
4、金融收益“偏度”和“峰度”的动态拟合——条件偏度和峰度的波动性建模研究。为了有效地捕获收益率时间序列高阶矩动态特征,在考虑当前预期和波动性条件下,首先讨论了一维的动态偏度和峰度建模研究。其次,为了考察多个市场或多个金融资产之间的高阶矩风险度量问题,推导了高阶中心矩和协矩之间的关系,提出了能够有效解决维数灾祸问题的多维条件高阶矩模型。在多维分布基础上,采用动态条件相关性(DCC)和自回归条件密度技术,通过智能优化算法对条件高阶矩模型的时变参数进行估计。实证研究结果表明,多维条件高阶矩模型较好的拟合了收益率时间序列高阶矩动态特征,与之前的高阶矩模型相比,能够有效解决高阶矩模型的维数灾祸问题,表明该模型能够捕捉到我国多个市场之间高阶矩风险特征,提高多维条件高阶矩模型测度能力。在已实现协方差矩阵的基础上,利用高次变差推导了已实现高阶矩模型。为了对未来的波动特性加以预测,在考虑已实现高阶矩的特性下,建立了已实现高阶矩FIVAR模型。
5、不确定条件下考虑偏度和峰度的投资组合研究。通过分析传统投资组合理论的不足,在有偏t分布基础上讨论条件高阶矩投资组合,应用贝叶斯理论分析不确定条件下高阶矩风险及其在投资组合理论中的应用问题。应用MCMC对有偏t分布进行了参数估计和投资组合权重的优化。研究结果表明,考虑偏度和峰度会对投资组合策略产生重要的影响。参数不确定问题考虑了投资者期望效用,对投资组合理论有重要的实践意义。
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.
引文
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