看不懂答案中的公式

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：

26193

25193

27193

24193

解释：

A is correct.

考点：Mapping to Option Position

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

VaR_AT&T= 1.65 × 1% × 30 × 20000=9900

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

和讲义上的公式不一样，能否请老师讲答案公式每一项对应的数值含义说明一下，谢谢

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李坏_品职助教 · 2023年05月01日

嗨，努力学习的PZer你好：

这道题是先分别求出两个option的VaR：

也就是用delta * 股票的VaR，比如 Microsoft股票的VaR= 1.65 × 2% × 120（这个是美金形式的VaR），再乘以delta 1000就得到了Microsoft option的VaR。

同理可以求出ATT期权的VaR。

再把两个期权的VaR组合起来，组合的公式原理其实和两种资产组合起来计算标准差是一样的：

组合标准差σ =( w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * ρ * w1 * w2 * σ1 * σ2)^(1/2)。

我们这里已经是美金形式的VaR，所以w1和w2这两个权重已经包含在金额里。

所以组合VaR= (VaR_mic ^2 + VaR_ATT^2 + 2 * ρ * VaR_mic * VaR_ATT)^(1/2)，这个求出来的是1-day VaR, 题目让求5天的，再乘以根号5就行了。

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看不懂答案中的公式

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