多项条件下收益率的分布及其应用研究

【作者】 罗荣华；

【导师】 肖春来；

【作者基本信息】 北方工业大学 ， 数量经济学， 2008， 硕士

【摘要】 股票收益率的分布是现代金融理论中的一个极其重要概念。一般认为,大多数股票的收益率服从正态分布,这些正态分布假设收益率的分布与价格无关,证券市场是一个有效的市场。然而,在文献[6]中,肖春来等认为由于市场内外部条件的变化,往往使收益率的统计分布特征发生变化,从而使传统的风险理论在实际应用中受到限制。因此,目前假定某种证券的收益率的统计分布特征在一定时期内基本稳定不符合实际的市场情况。他们以股票市场为例,提出价格条件收益率的思想,即在一定价格水平上的收益率。实际上,在文献[7]中,柴文义等通过对国内外股票市场的研究,结果表明股票收益率与股票价格存在弱的负相关关系。在此基础上,文献[8]在股票收益率和价格对数服从二元联合正态分布的假设下,推导出了价格条件下的股票收益率分布特征表达式和VaR_t的计算方法。然而,即便如此,由于股票市场瞬息万变,其收益率受到多种因素的影响。价格条件下收益率分布特征中的价格均值μ、方差σ~2和自相关系数ρ就再不能被看作是常数,而应该将其当成变量,即μ_t、σ_t~2和ρ_t,以使收益率的分布特征更符合市场实际。因此,研究多项条件下收益率的分布就显得尤为重要和紧迫。本文首先详细分析了价格条件下收益率分布在VaR中的应用情况,得出了应将价格均值μ、方差σ~2和自相关系数ρ看成变量而不是常量的结论,而且可用移动平均法达到这一目的;其次,经过对20支股票大量的实证研究,初步确定了移动平均期数的范围,且初步表明收益率分布不仅仅决定于价格,还决定于价格均值μ、方差σ_t~2和自相关系数ρ_t等变量,即收益率服从多项条件分布;再次,为了使价格均值μ、方差σ_t~2和相关系数ρ_t更具预测性,更好的应用于实际,本文对它们分别建立了预测模型;最后,将预测模型应用于VaR_t的计算,并对其预测效果进行了检验。结果表明,用预测值计算的VaR_t值较用移动平均值计算的VaR_t值更准确,这也进一步表明收益率服从多项条件分布。更多还原

【Abstract】 The distribution of the stock yield is an extremely important concept of modern financial theory.It is generally believed that most stocks possess normal distribution,the stock yield distribution has nothing to do with price,and the stock market is effective.But in paper[6],Xiao Chun-lai,etc,assumed that the conditional distribution theory will encounter difficulties in application of the risk theory because of the changed statistical characters of the distribution which is changing as the external and internal conditions of stock market are changing. Therefore,the hypothesis that the statistical characters of stock yield distribution are stable in a certain period of time is not fitted with the actual market situation. In fact,in paper[7],CHAI Wen-yi points that the stock price has some weakly negative relation with stock yield by studying native and foreign stock markets. Xiao Chun-lai,CHAI Wen-yi have gotten the formulas of the statistical characters of stock yield distribution and VaR_t based on the hypothesis that the stock yield and price possess the joint normal distribution in paper[8].However,as the stock market is changing time in time and full of complexities,the stock yield is affected by many factors.The mean priceμ, varianceσ~2 and the autocorrelation coefficientρin the stock yield distribution determined by price can no longer be seen as constant,but variables,that isμ~2,σ_t~2 andρ_t,which makes the stock yield distribution more fitted with the actual market.Therefore,studying the stock yield distribution determined by multi- conditions is particularly important and urgent.In this paper the inaccuracy of VaR brought by the stock yield distribution determined by the stock price is firstly analyzed.The result is that the mean priceμ,varianceσ~2 and autocorrelation coefficientρshould be seen as variables rather than the constant which can be achieved by using moving average method.Secondly,through studying 20 stocks,we initially specified the moving-average range,and it initially demonstrates that the stock yield distribution is not only determined by the price,but also by the mean priceμ_t, varianceσ_t~2 and autocorrelation coefficientsρ_t.That is,the stock yield distribution possesses multi-conditional distribution.Thirdly in order to make the price meanμ_t,varianceσ_t~2 and autocorrelation coefficientsρ_t predictable and practical,their predicted models are set up in this paper.Lastly the predicted models are used to calculate VaR_t,and their predicted effects had been tested.The results show that,the VaR_t calculated by the predicted value is more accurate than that of calculated by the moving average value,which further shows that the stock yield possesses the multi-conditional distribution.更多还原