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13995173783 · 2023年06月12日

本题中该步骤是什么意思？

  1. FRM I
  2. Quantitative

NO.PZ2019040801000027

问题如下：

The price percent changes of stock X and Y were 5.0% and 1.0%, respectively. The correlation estimate based on the historical data of the two on day n-1 is 0.6, the estimated standard deviations of price of X and Y on day n-1 were 2.3% and 1.7%, respectively. Suppose the analyst uses the EWMA model with λ = 0.97 to update the correlation and covariance. What is the new estimate of the correlation between X and Y on day n?

选项：

A.

0.34.

B.

0.42.

C.

0.60.

D.

0.68.

解释：

C is correct.

考点：EWMA模型

解析：先计算day n-1时候的协方差：

cov(X, Y) = ΡX,Y x σXσY = 0.6 * 2.3% * 1.7% = 0.000235

然后通过EWMA模型

估计day n的协方差：covn = 0.97 * 0.000235 + 0.03 * 5% * 1% = 0.00024295

估计X的方差：σ2X,n = 0.97 x 0.023^2 + 0.03 x 0.05^2 = 0.00058813

X的标准差就是0.00058813^0.5=0.02425

估计Y的方差：σ2Y,n = 0.97 x 0.0172 + 0.03 x0.012 = 0.0003078 + 0.000003 = 0.0002833

Y的标准差就是0.0002833^0.5=0.01683

最后新的相关系数就是协方差除以X标准差再除以Y的标准差：

0.00024295/（0.02425*0.01683）=0.5952

估计day n的协方差：covn = 0.97 * 0.000235 + 0.03 * 5% * 1% = 0.00024295

这步是什么意思？具体使用的公式是哪个公式？XY的协方差不是已经在上一步计算出来是0.000235吗？此处的协方差是什么的协方差？

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DD仔_品职助教 · 2023年06月13日

嗨，努力学习的PZer你好：


同学你好，

这提考察的是EWMA，这个公式是EWMA计算cov的公式，请看下图：

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

13995173783 · 2023年06月13日

谢谢老师

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NO.PZ2019040801000027问题如下The pripercent changes of stoX anY were 5.0% an1.0%, respectively. The correlation estimate baseon the historicta of the two on y n-1 is 0.6, the estimatestanrviations of priof X anY on y n-1 were 2.3% an1.7%, respectively. Suppose the analyst uses the EWMA mol with λ = 0.97 to upte the correlation ancovariance. Whis the new estimate of the correlation between X anY on y n?A.0.34.B.0.42.C.0.60.0.68.C is correct.考点EWMA模型解析先计算y n-1时候的协方差cov(X, Y) = ΡX,Y x σXσY = 0.6 * 2.3% * 1.7% = 0.000235然后通过EWMA模型估计y n的协方差covn = 0.97 * 0.000235 + 0.03 * 5% * 1% = 0.00024295估计X的方差σ2X,n = 0.97 x 0.023^2 + 0.03 x 0.05^2 = 0.00058813X的标准差就是0.00058813^0.5=0.02425估计Y的方差σ2Y,n = 0.97 x 0.0172 + 0.03 x0.012 = 0.0003078 + 0.000003 = 0.0002833Y的标准差就是0.0002833^0.5=0.01683最后新的相关系数就是协方差除以X标准差再除以Y的标准差0.00024295/（0.02425*0.01683）=0.5952老师好，请问EWMA和GARCH的covariance是在课程哪里讲的呢？看了下笔记和课程没找到。

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