ab那个是算什么的

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 2 years using the Gaussian default time copula under the assumption that a 1-year Gaussian default correlation is 0.36. The fund reports that x_BB and x_B are abscise values of the bivariate normal distribution presented in the table below where

xBB = N^-1 (QBB(tBB)) and xB= N-1(QB(tB)) with tBB and tB being the time-to-default of BB-rated and B-rated companies respectively; and QBB and QBB being the cumulative distribution functions of tBB and tB, respectively; and N denotes the standard normal distribution; and M denotes the joint bivariate cumulative standard normal distribution:

Applying the Gaussian copula, which of the following corresponds to the joint probability that firm RST and firm WYZ will both default before the end of year 2?

选项：

A.

M(x_BB = 0.0612) + M(x_B = 0.1063) – M(x_BB = 0.0612)*M(x_B = 0.1063)

B.

M(xBB = 0.1133) + M(xB = 0.2969) – M(xBB =0.1133)*M(xB = 0. 0.2969)

C.

M(x_BB ≤ 0.1133 ∩ x_B ≤ 0.2969)

D.

M(x_BB ≤ -1.209 ∩ x_B ≤ -0.533)

解释：

中文解析：

RST和WYZ会同时在第二年年末违约的联合概率是多少？

如下公式所示：

𝑃{[𝑡BB ≤ 2] ∩ [𝑡B ≤ 2]} = 𝑃{[𝑁-1 (𝑄BB (𝑡BB)) ≤ 𝑁-1 (𝑄BB(2))] ∩ [𝑁-1 (𝑄B (𝑡B )) ≤ 𝑁-1 (𝑄B (2))]} = 𝑃{[𝑋BB ≤ −1.209] ∩ [𝑋B ≤ −0.533]}

D is correct.

The required probability is:

𝑃{[𝑡_BB ≤ 2] ∩ [𝑡_B ≤ 2]} = 𝑃{[𝑁^-1 (𝑄_BB (𝑡BB)) ≤ 𝑁^-1 (𝑄BB(2))] ∩ [𝑁-1 (𝑄_B (𝑡_B )) ≤ 𝑁-1 (𝑄_B (2))]} = 𝑃{[𝑋_BB ≤ −1.209] ∩ [𝑋_B ≤ −0.533]}