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滴滴姐姐~ · 2021年09月02日

问一道题(mapping VaR吧)

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

VaRMic= 1.65 × 2% × 120 × 1000 = 3960

VaRAT&T= 1.65 × 1% × 30 × 20000=9900

这两步看懂了,但我理解的是说这里我们求的是这两只股票的option的VaR,对吧?


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

那这里怎么能用股票之间的correlation代替option之间的correlation捏?


一脸懵逼.jpg(我可能是一级太久以前了。。。难道这是一级必备知识点0.0)

4 个答案
已采纳答案

品职答疑小助手雍 · 2021年09月02日

嗨,爱思考的PZer你好:


“我理解的是说这里我们求的是这两只股票的option的VaR,对吧?” 对的,先求出两个option的var。

后面股票的correlation是可以代替option的correlation的,因为correlation有一个性质,就是x和y的correlation 和 ax和by的correlation是一样的,所以这里先mapping后correlation依旧可以直接拿来用。

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努力的时光都是限量版,加油!

滴滴姐姐~ · 2021年09月02日

x和y的correlation 和 ax和by的correlation是一样的? 瑞类?rho(ax, by) = rho(x,y)? 这超出认知了 能不能详细讲讲~ 谢谢少年!!~

品职答疑小助手雍 · 2021年10月18日

同学你好,这道题的考点就是通过var mapping求出两个个股的分别的var,然后通过两者的相关性求两个个股组成组合的var。如果那个点或者步骤不明白可以针对性的提问。

dannyni · 2021年10月17日

不太懂这题的考点

品职答疑小助手雍 · 2021年09月02日

嗨,爱思考的PZer你好:


这确实是1级数量里的,我举个简单的例子吧,就是Y=x这条直线,上的点是x=1,2,3时y=1,2,3,这条线百分百拟合的,也就是最小二乘法可以直接划出来一条线没有线外的点,也就是ρ=1。

现在x变成0.5x了,也就是x=0.5,1,1.5时y=1,2,3,这条线还是百分百拟合了,只不过这条线变成了y=2x。最小二乘法也可以直接划出来一条线没有线外的点,是ρ还是=1。

不管你x和y呈什么倍数变动,他俩的ρ都是x和y的ρ。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

滴滴姐姐~ · 2021年09月02日

直呼优秀!!!学到了学到了!!!

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