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fdzh · 2023年11月13日

请问这题的知识点是?

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:

完全不会做

1 个答案

品职答疑小助手雍 · 2023年11月14日

同学你好,我觉得这题不太建议掌握了,虽然原版书提到了但是计算量上和难度上都不太适合出题。

讲义只做了简要的讲解见470页。

原理是第一步根据违约和不违约假设违约这个情况服从二项分布,所以二项分布的方差是p*(1-p),再算上面值和LGD算出单个债券违约损失的标准差68,585.71。

第二步是结合讲义470页组合的风险来的,最终组合的方差是n*σ方+n*(n-1)*ρ*σ

最后得到的公式就是(这个推导过程在原版书74页,学有余力可以去了解一下)