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水瓶公主 · 2023年04月03日

var组合由标得资产组成

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2016082404000039

问题如下：

An investor is long a short-term at-the-money put option on an underlying portfolio of equities with a notional value of USD 100,000. If the 95% VAR of the underlying portfolio is 10.4%, which of the following statements about the VAR of the option position is correct when second-order terms are considered?

选项：

A.

  The VAR of the option position is slightly more than USD 5,200.

B.

  The VAR of the option position is slightly more than USD 10,400.

C.

  The VAR of the option position is slightly less than USD 5,200.

D.

  The VAR of the option position is slightly less than USD 10,400.

解释：

ANSWER: C

The delta must be around 0.5, which implies a linear VAR of $100,000×10.4%×0.5=$5,200.\$100,000\times10.4\%\times0.5=\$5,200.The position is long an option and has positive gamma. As a result, the quadratic VAR must be lower than $5,200.

解析：

有一个投资者买了一个ATM的put option，基础资产是一个股票组合，金额为100000美元。如果基础资产95%VaR是10.4%，请问下面关于这个option考虑到非线性关系的VaR正确的是哪一个？

ATM put的delta=0.5

线性关系的option的VaR=S*delta*VaR=100,000*0.5*10.4%=5200

考虑到二次关系的VaR是在线性关系的基础上减去一个数值，所以会低于5200.

var组合=delta✖️var标的资产


10.4=0.5*varoption

所以不是10.4/0.5吗

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1 个答案

李坏_品职助教 · 2023年04月03日

嗨，努力学习的PZer你好：


题目告诉我们股票的VaR是10.4%，由于ATM put的线性关系的VaR = S * Delta * 股票的VaR = 100,000 * 0.5*10.4% = 5200，如果加入了 second-order term，那么ATM put的VaR = S * Delta * 股票的VaR - 二次项（二次项一定是大于0的，因为是平方项），所以这个VaR肯定小于5200。所以选C。


你写的不太对，应该是线性关系的VaR = 100,000 * 0.5 * 10.4%。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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