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Jenny · 2021年04月10日

WCL的计算没懂

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2016082406000083

问题如下：

A risk analyst is trying to estimate the credit VAR for a risky bond. The credit VAR is defined as the maximum unexpected loss at a confidence level of 99.9% over a one-month horizon. Assume that the bond is valued at $1,000,000 one month forward, and the one-year cumulative default probability is 2% for this bond. What is the best estimate of the credit VAR for the bond, assuming no recovery?

选项：

A.

$20,000

B.

$1,682

C.

$998,318

D.

$0

解释：

ANSWER: C

First, we have to transform the annual default probability into a monthly probability. Using (1−2%)=(1−d)12{(1-2\%)}={(1-d)}^{12}, we find d=0.00168, which assumes a constant probability of default during the year. Next, we compute the expected credit loss, which is d×$1,000,000=$1,682d\times\$1,000,000=\$1,682. Finally, we calculate the WCL at the 99.9% confidence level, which is the lowest number \(CL_i\)such that P(CL≤CLi)≥99.9%P{(CL\leq CL_i)}\geq99.9\%. We have P(CL=0)=99.83%P{(CL=0)}=99.83\%; P(CL≤1,000,000)=100.00%P{(CL\leq1,000,000)}=100.00\%. Therefore, the WCL is $1,000,000, and the CVAR is $1,000,000−$1,682=$998,318\$1,000,000-\$1,682=\$998,318.

不记得课上有提到过这个计算，可以具体讲一下吗？然后对应讲义具体的哪个部分？
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1 个答案

品职答疑小助手雍 · 2021年04月10日

嗨，从没放弃的小努力你好：


这题涉及对概念的理解和运用的，单纯的课上的概念其实都懂的，不过这题理解上涉及WCL的含义，以及月PD和年PD的转换。

首先，月PD和年PD的转换：题目给了年PD是2%，也就是1-0.02，代表一年不违约的概率；一年不违约也就意味着连续12个月不违约，假设月PD是d的话，12个月连续不违约的概率就是（1-d）的12次方。连续12个月不违约的概率和1年不违约的概率是相等的，即1-0.02 = (1-d)的12次方。

然后是WCL的含义：前一步算了月PD是0.168%，也就是那么单个月来说在0.168%概率的情况下，会发生1 million的损失；而1- 0.168% = 99.832%的概率下，是不发生损失的。而题目要求的confidence level是99.9%，超过的99.832%这个数（也可以理解成在被包含在最尾部的那0.168%的概率里，损失是1million），所以WCL=1million。

而Credit var是等于WCL-EL的，所以答案就是C了。


PS：如果题目要求的confidence level是小于99.832%的，比如99%，那WCL就等于0了，此时credit var（按公式是负数，但是var不能为负，否则就是收益了）也就等于0了。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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2020-10-14 10:23 1 · 回答

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2020-09-20 16:51 1 · 回答

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2020-08-17 00:23 2 · 回答

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2020-03-21 16:20 1 · 回答