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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年06月12日

基础班只讲过volatility的EWMA model，没讲过correlation和covariance的EWMA model

  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

助教你好：


一：基础班讲的ARCH, EWMA, GARCH model全是关于volatility，所有例题也是关于volatility，而这题涉及到的东西为什么没在基础班里面讲过？


二：这题所说的东西是指下方框架图这个知识吗？框架图上这块内容根本没出现在基础班讲义里面。



基础班是漏了东西？还是这框架图和题目是多余的东西？

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1 个答案

李坏_品职助教 · 2023年06月12日

嗨，从没放弃的小努力你好：


所谓的相关系数就是协方差除以X标准差再除以Y的标准差：


所以预测相关系数，本质是就是在预测volatility。


强化班的框架图的EWMA，和基础班讲义下图的EWMA公式原理一样，只是把基础班里面的σ^2换成cov：

σ^2_n-1是n-1天的方差，这个替换为n-1天的协方差。

然后u^2_n-1是n-1天的 price percent change的平方，替换为X的 price percent change乘以Y的 price percent change。


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努力的时光都是限量版，加油！

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