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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 X_BB and X_B are abscise values of the bivariate normal distribution presented in the table below where X_BB = N^-1(Q_BB(t_BB)) and X_B= N^-1(Q_B(t_B)) with t_BBand t_B being the time-to-default of BB-rated and B-rated companies respectively; and Q_BB and Q_B being the cumulative distribution functions of t_BB and t_B , respectively; and N denote the 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?

AQ(XBB = 0.0612) + Q(XB = 0.1063) – Q(XBB = 0.0612)*Q(XB = 0.1063）

BQ(XBB = 0.1133) + Q(XB = 0.2969) – Q(XBB = 0.1133)*Q(XB = 0.2969)

CQ(XBB ≤ 0.1133 ∩XB ≤ 0.2969)

DQ(XBB ≤ – 1.209 ∩ XB ≤ –0.533)

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