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Shuangshuang · 2024年07月27日

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  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2024042601000038

问题如下：

Becky the Risk Analyst is trying to estimate the credit value at risk (CVaR) of a three-bond portfolio, where the CVaR is defined as the maximum unexpected loss at 99.0% confidence over a one-month horizon. The bonds are independent (i.e., no default correlation) and identical with a one-month forward value of $1.0 million each, a one-year cumulative default probability of 4.0%, and an assumed zero recovery rate. Which is nearest to the one-month 99.0% CVaR?

选项：

A.

$989,812

B.

$1.0 million

C.

$1.7 million

D.

$2.3 million

解释：

The one-month PD = 1 - (100% - 4%)(1/12) = 0.3396%.

Expected loss = 98.9846% × 0 + 1.0119% × $1.0 million + 0.0034% × $2.0 million + 0% × $3.0 million = $10,188

The probability of zero defaults = (1 - 0.3396%)3 = 98.98464%.

Therefore, the 99.0% WCL is one default or $1.0 million, and

the 99.0% CVaR = $1.0 million - $10,188 = $989,812.

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已采纳答案

pzqa27 · 2024年07月28日

嗨，爱思考的PZer你好：


这个题是要是99%的VaR,那么就是用WCL-EL就可以了，所以这个题分成2部分，第一部分是计算WCL，第二部分是计算EL。EL的计算就是 98.9846% × 0 + 1.0119% × $1.0 million + 0.0034% × $2.0 million + 0% × $3.0 million = $10,188

然后是WCL的确定，由于题目要求是99%的VaR,而一个月的违约率是0.3396%，那么根据谨慎性原则，99%WCL对应的应该是1个月的违约，所以应该是1m.

最后就是用1m-10188既可以得到正确答案。

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