Financial Risk Manager Part 2
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A hedge fund operating under a distressed securities strategy is currently assessing the solvency risk of two potential investment targets. As of now, firm RST holds a credit rating of BB, while firm WYZ is rated B. The hedge fund intends to determine the probability that both firms will simultaneously default within the next 2 years, applying a Gaussian default time copula model. The analysis assumes a 1-year Gaussian default correlation of 0.36. The fund has provided a table containing the abscissa values X and xg from the bivariate normal distribution. Specifically, XBB is defined as N^-1(QBB(tgB)) and Xg is defined as N^-1(Qe(t)), where tgB and tg represent the time-to-default for BB-rated and B-rated companies, respectively; QBB and Q denote the cumulative distribution functions for tBB and tg, respectively; and N denotes the standard normal distribution, while M represents the joint bivariate cumulative standard normal distribution:
Firm RST Firm WYZ Firm RST Firm WYZ Cumulative Default Probability Cumulative Default Probability Standard Normal Percentiles Standard Normal Percentiles Year Qe(t) QBB(t) N^-1(QBB(t)) 1 5.21% 5.21% -1.625 2 6.12% 11.33% -1.209 3 5.50% 16.83% -0.961 4 4.81% 21.64% -0.784 5 4.22% 25.86% -0.648
Using the Gaussian copula approach, which option correctly represents the joint probability that both firm RST and firm WYZ will default before the end of year 2?
A hedge fund operating under a distressed securities strategy is currently assessing the solvency risk of two potential investment targets. As of now, firm RST holds a credit rating of BB, while firm WYZ is rated B. The hedge fund intends to determine the probability that both firms will simultaneously default within the next 2 years, applying a Gaussian default time copula model. The analysis assumes a 1-year Gaussian default correlation of 0.36. The fund has provided a table containing the abscissa values X and xg from the bivariate normal distribution. Specifically, XBB is defined as N^-1(QBB(tgB)) and Xg is defined as N^-1(Qe(t)), where tgB and tg represent the time-to-default for BB-rated and B-rated companies, respectively; QBB and Q denote the cumulative distribution functions for tBB and tg, respectively; and N denotes the standard normal distribution, while M represents the joint bivariate cumulative standard normal distribution:
| Firm RST | Firm WYZ | Firm RST | Firm WYZ |
|---|---|---|---|
| Cumulative Default Probability | Cumulative Default Probability | Standard Normal Percentiles | Standard Normal Percentiles |
| Year | Qe(t) | QBB(t) | N^-1(QBB(t)) |
| 1 | 5.21% | 5.21% | -1.625 |
| 2 | 6.12% | 11.33% | -1.209 |
| 3 | 5.50% | 16.83% | -0.961 |
| 4 | 4.81% | 21.64% | -0.784 |
| 5 | 4.22% | 25.86% | -0.648 |
Using the Gaussian copula approach, which option correctly represents the joint probability that both firm RST and firm WYZ will default before the end of year 2?