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Shuangshuang · 2024年08月01日

不懂

NO.PZ2023100703000073

问题如下:

A hedge fund that runs a distressed securities strategy is evaluating the solvency conditions of two potential investment targets. Currently firm RST is rated BB and firm WYZ is rated B. The hedge fund is interested in determining the joint default probability of the two firms over the next two years using the Gaussian default time copula under the assumption that a one-year Gaussian default correlation is 0.36. The fund reports that xBB and xB are mapped abscise values of the bivariate normal distribution presented in the table below, while Q and N denote the cumulative default probability and the standard normal distribution, respectively:


Applying the Gaussian copula, which of the following best describes the derivation of the joint probability(Q) that firm RST and firm WYZ will both default in year 2?

选项:

A.Q(xBB = 0.0612) + Q(xB = 0.1063) – Q(xBB = 0.0612)*Q(xB = 0.1063) B.Q(xBB = 0.1133) + Q(xB = 0.2969) – Q(xBB = 0.1133)*Q(xB = 0.2969) C.Q(xBB≤0.1133∩xB≤0.2969) D.Q(xBB ≤-0.8586∩xB≤-0.2630)

解释:

The joint probability of default is measured by “cumulative standard normal percentiles.” What the copula function does is to: first, map the cumulative default probability values (marginal distributions) of a multivariate distribution - percentile to percentile - to a cumulative standard normal distribution. Then, second, find the mapped abscise (x-axis) values of the cumulative standard normal distribution. The Gaussian copula procedure essentially assumes that only a single correlation (not a correlation matrix) can now be applied to the multivariate distribution.

standard normal percentiles那列是什么意思啊,怎么判断看哪列

1 个答案
已采纳答案

李坏_品职助教 · 2024年08月01日

嗨,努力学习的PZer你好:


首先N(x)表示标准正态分布累计概率函数,当x = 1.645时,N(x) = 0.95,说明横坐标x ≤ 1.645对应的累计概率是0.95.

表格第四列和最后一列写的是N^-1,这表示标准正态分布概率函数的反函数。也就是N^-1 (0.95) = 1.645. 这也可以说明x ≤ 1.645对应的累计概率是0.95。


表格里第二行、最后一列数字是-0.2630,参考我上面说的原理,这表示x1 ≤ -0.2630的概率是QB(t),而这个QB(t)对应的就是WYZ公司在第二年的违约概率29.69%(第二行、倒数第二列)

同理,第二行、第四列数字是-0.8586,这表示x2 ≤ -0.8586对应的概率是QBB(t),也就是RST公司在第二年的违约概率

11.33%。


题目最后问的是这俩公司都在第二年违约的联合概率该如何用两个x来表示?那也就是x1 ≤ -0.2630并且x2 ≤ -0.8586,也就是D选项。

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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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