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。。 · 2025年07月09日

关于二项分布和泊松分布

NO.PZ2023091601000028

问题如下:

Afixed income portfolio manager currently holds a portfolio of bonds of variouscompanies. Assuming all these bonds have the same annualized probability ofdefault and that the defaults are independent, the number of defaults in thisportfolio over the next year follows which type of distribution?

选项:

A.

Bernoulli

B.

Normal

C.

Binomial

D.

Exponential

解释:

The result wouldfollow a Binomial distribution as there is a fixed number of random variables,each with the same annualized probability of default. It is not a Bernoullidistribution, as a Bernoulli distribution would describe the likelihood ofdefault of one of the individual bonds rather than of the entire portfolio(i.e. a Binomial distribution essentially describes a group of Bernoullidistributed variables). A normal distribution is used to model continuousvariables, while in this case the number of defaults within the portfolio isdiscrete.

考察违约次数即为离散分布,由于银行贷款数量一般较多,优先考虑泊松分布,若无泊松分布,退而求其次选择正态分布,一般也不会有二项分布与泊松分布两个选项吧 考察违约时间间隔时用指数分布

1 个答案

李坏_品职助教 · 2025年07月09日

嗨,爱思考的PZer你好:


是的。一般情况下,如果试验次数较少,问你违约概率,可以用二项分布。但是如果试验次数很多(就是债券数量或者贷款数量很多),优先考虑泊松分布。 这种题目都会给你泊松分布或者二项分布的选项的,要不然就没有考察意义了。


如果问你违约时间长度 考虑指数分布。


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