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根据多元t分布的定义及性质,推导出二维t分布随机变量差的条件分布仍服从t分布.在假定股票价格对数与收益率服从二维t分布的基础上,利用该性质,可以得到不同股票价格水平条件下,收益率的一维条件t分布,进而计算出价格条件VaR.利用多元t分布研究价格条件的收益率分布问题,与正态分布相比,较好地刻画了证券收益率分布的尖峰厚尾现象.
According to the definition and property of multivariate t distribution, it is deduced that the conditional distribution of the difference of two-dimensional t-distribution random variables is still subject to the t distribution.Based on the assumption that the stock price logarithm and the return rate obey the two-dimensional t distribution, Under the condition of different stock price level, the one-dimensional conditional t distribution of the return rate, and then the VaR of the price condition are calculated.Using the multivariate t-distribution to study the distribution of the return rate under the price condition, the stock returns better than the normal distribution Rate distribution of the peak thick tail phenomenon.