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徐威廉 · 2024年10月26日

WCL怎么确定的是99%就在1m 和 0m之间？

  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.

WCL怎么确定的是99%就在1m 和 0m之间？怎么画的分布？

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pzqa27 · 2024年10月28日

嗨，从没放弃的小努力你好：


98.98464%.已经很接近99%， 那如果再累加上一个债券违约的概率，肯定超过99%了，所以根据保守性原则，选择1M作为WCL

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

徐威廉 · 2024年10月30日

98.98464%这个概率是0个债券违约的概率啊，这为什么是WCL的违约概率，WCL的违约概率应该是最差情景的3个债券全部违约PD=0%

pzqa27 · 2024年10月30日

嗨，爱思考的PZer你好：


WCL的算法是把损失从小到大累积到99%， 最小的情况就是没有债券违约，那么这种概率是98.98464%，第二小的是违约一个债券，累积违约概率超过了99%， 所以WCL 选1m

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努力的时光都是限量版，加油！

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