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梦梦 · 2024年11月12日

UL（p）的推导

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023091701000134

问题如下：

A risk analyst at a bank is estimating the distribution of credit losses for a portfolio of 30 identical loan exposures. The analyst assumes that the credit losses follow a binomial distribution. Each loan has the following characteristics:

• Amount: SGD 500,000

• Probability of default: 4%

• Recovery rate: 30%

• Average pairwise default correlation: 0.4

What is the standard deviation of losses on the loan portfolio expressed as a percentage of the size of the portfolio?

选项：

A.3.8%

B.5.8%

C.7.8%

D.8.9%

解释：

The standard deviation of losses for each individual loan is:

where p represents probability of default, Li represents exposure at default (amount borrowed), and Ri represents recovery rate.

The standard deviation of losses on the portfolio of n loans as a percentage of its size is then calculated as:


组合的UL不应该是这个吗？

第一张图的分母，L*n^0.5咋来的啊？

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已采纳答案

李坏_品职助教 · 2024年11月12日

嗨，从没放弃的小努力你好：


是的，是要除以n*L

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

梦梦 · 2024年11月12日

好的，谢谢

李坏_品职助教 · 2024年11月12日

嗨，从没放弃的小努力你好：


推导过程可以参考原版书教材：

贷款组合P中有n个贷款，

组合P的方差和标准差（此处计算的α，表示的是组合标准差占贷款金额的比例）：

假设所有的贷款金额都相等（每个贷款金额都是L），那么分母这个∑Li = n*L。

再假设所有贷款的违约概率、赔偿比例都相等，那么组合的方差可以简化为：

所以α 可以写成：

本题最后问的也就是α。


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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！

梦梦 · 2024年11月12日

等于我图中的公式再除以n*L（笔*每笔贷款金额）就和您的公式一样了

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