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pinzhixiaoguo · 2022年09月19日

请问mapping里面VAR(△S)?

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

首先请老师看我这个理解对不对:

此题分3步:

第一步,求单个股票的VAR;

第二步,利用单个股票的VAR采用mapping的方法求期权的VAR;

第三步,用两个期权的VAR求组合的VAR。


如果上述理解是正确的。那么,在mapping求期权的VAR的时候有两个问题:

第一个问题,课上学的是VAR(△c)=delta乘以VAR(△S),也就是需要知道资产价格变动对应的VAR,而我们第一步求的是单个股票的VAR,也就是S的VAR,这个S的VAR和△S的VAR是一个VAR吗,就随便往第二步的mapping里面套用?


第二个问题,课上学的是call opt的公式,那如果是put的公式也是一样吗?

Potatowpn · 2023年01月19日

请问求delta S价格变动的VAR的知识点在哪一章节?

2 个答案

DD仔_品职助教 · 2023年01月19日

嗨,努力学习的PZer你好:


同学你好,

这是我们VAR mapping的内容,在基础版讲义71页开始。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

DD仔_品职助教 · 2022年09月20日

嗨,从没放弃的小努力你好:


步骤是正确的。

第一个问题,我们求的就是delta S价格变动的VAR,不是S的,具体公式:VaR(dS)=区间调整*σ*日子调整*价格,就是前两步。

第二个问题,put和call一样,因为delta取得是绝对值,put的delta是负数,call是正数,取了绝对值之后一样的

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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