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Miracle_ · 2023年01月29日

CF mapping要不要考虑相关系数?

NO.PZ2018122701000049

问题如下:

A portfolio consists of options on Microsoft and AT&T. The options on Microsoft have a delta of 1000, and the options on AT&T have a delta of 20000. The Microsoft share price is $120, and the AT&T share price is $30. Assuming that the daily volatility of Microsoft is 2% and the daily volatility of AT&T is 1% and the correlation between the daily changes is 0.3, the 5-day 95% VaR is

选项:

A.

26193

B.

25193

C.

27193

D.

24193

解释:

A is correct.

考点:Mapping to Option Position

解析:VaRMic= 1.65 × 2% × 120 × 1000 = 3960

VaRAT&T= 1.65 × 1% × 30 × 20000=9900

VARP(5day,95%)=39602+99002+2×0.3×3960×9900×5=26193VAR_{P(5-day,95\%)}=\sqrt{3960^2+9900^2+2\times0.3\times3960\times9900}\times\sqrt5=26193

讲义75页表格的第三列算undiversifield VaR直接把每笔CF的VaR相加了,不用像本题一样,考虑每笔CF/各类标的的相关性吗?

1 个答案
已采纳答案

李坏_品职助教 · 2023年01月29日

嗨,爱思考的PZer你好:


这一题不是CF mapping,它是一个投资组合,包含了两种option,所以计算VaR要考虑两个option之间的相关性。


讲义里例题的第三列计算了undiversified VaR,这个是不考虑相关系数的VaR。

然后最后一列还计算了component VaR,最后一列的这个component VaR考虑了相关系数:

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