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410140980 · 2023年07月02日

copula函数mapping的不是marginal distribution吗

NO.PZ2020033001000048

问题如下:

Construct a Gaussian copula to estimate the joint default probability of two assets within a year. Regarding to this copula, which of the following statements are correct?

I.This copula uses a correlation matrix to define the relationship between variables.

II.This copula requires that the respective cumulative default probability are mapped to a bivariate standard normal distribution.

III.This type of copula is widely applied in finance.

IV.The N11(Q1(t))N_1^{-1}{(Q_1{(t)})} maps the individual asset cumulative default probability to standard normal.

选项:

A.

I and II

B.

II and III

C.

I, II and III

D.

II, III and IV

解释:

D is correct.

考点:copula function

解析:

表述1 错误:当只有两个资产时,此时只有一个相关系数 ρ,不需要相关系数矩阵(correlation matrix) 。

老师在讲copula的时候,基础班视频听懂了,做相关copula函数的题目就有点混乱,搞不清什么时候选择marginal distribution,什么时候选择cumulative distribution

1 个答案

DD仔_品职助教 · 2023年07月03日

嗨,从没放弃的小努力你好:


同学你好,

这其实就是再考阅读理解了,d选项想说的是对于一个单一资产来说,一个参数输入就足够得到累计分布值。

通过公式来理解的话请看下图:

因为copulas的目的是简化统计模型的,最后表达式中G 那个函数代表的是 marginal distributions,然后M代表的是联合累计分布函数。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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