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Archie · 2023年04月26日

VAR组合公式

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

老师您好,

我能明白题目的解法。但是在做的时候,我突然想尝试用miu ≠ 0 的那种带权重的方式求解。这里的权重应该怎么计算呢。麻烦老师解答。我的直觉是用金额直接放进去算,但是好像又不太对

2 个答案

DD仔_品职助教 · 2023年07月04日

嗨,努力学习的PZer你好:


这题用的是第二个求optionVaR的公式

因为这两个资产的delta不一样,所以必须在计算组合σ的时候考虑,而不能是在计算VaR的时候再统一考虑。

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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!

DD仔_品职助教 · 2023年04月27日

嗨,从没放弃的小努力你好:


同学你好,

像这种直接问金额的题,不建议你先求出权重然后再求组合VaR再计算,因为很复杂会出错,而且计算出权重再乘很浪费做题的时间,完全没必要的。

下面给同学介绍两种对于直接是求金额的这种题的两种做法,这两种做法相对于求出权重会更快,而且也不容易出错:


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加油吧,让我们一起遇见更好的自己!

410140980 · 2023年07月04日

老师第二种方法计算的组合的标准差σp,各自资产的标准差的平方为什么还乘以了delta,这里我有点懵,

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