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和棋 · 2021年02月18日

Var的直接相加和平方根法相加有什么区别?

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

如题

1 个答案
已采纳答案

袁园_品职助教 · 2021年02月19日

同学你好!

线性关系才能直接叠加,但VaR是由σ算出来的,σ之间不是线性关系,不能直接相加。

直接适用平方根法则的是σ,而不是VaR。即原始的关系是Annual σ=√252×daily σ

VaR适用平方根法则的前提是假设了均值μ=0。这个假设下才有Annual VaR=√252×daily VaR。

这是因为此时VaR=|μ-z*σ|=|z*σ|=|z|*σ。所以Annual VaR=|z|*Annual σ;Daily VaR=|z|*Daily σ;

由于Annual σ=√252×daily σ,所以Annual VaR=|z|*Annual σ=|z|*√252×daily σ=√252×daily VaR

可以看出此时VaR适用平方根法则的原因是:1)假设了μ=0;2)实质是公式里的σ适用了平方根法则。


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