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Q.1832 A pair of credits with BBB- and BBB+ ratings have default probabilities of 0.003 and 0.004, respectively. If the credits are correlated, what is the maximum allowed value of default correlation such that a portfolio composed of only two of these credits has a default probability of 0.2%? | Financial Risk Manager Part 2 Quiz - LeetQuiz

Explanation:

The joint default probability is given by the formula:

\pi_{12} = \rho_{12}\sqrt{\pi_1(1 - \pi_1)}\sqrt{\pi_2(1 - \pi_2)} + \pi_1\pi_2

Given $\pi_1$ and $\pi_2$ ,

0.2\% = \rho_{12}\sqrt{0.003(1 - 0.003)}\sqrt{0.004(1 - 0.004)} + 0.003 \times 0.004

\Rightarrow \rho_{12} = 0.5774 = 57.59\%

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Q.1832 A pair of credits with BBB- and BBB+ ratings have default probabilities of 0.003 and 0.004, respectively. If the credits are correlated, what is the maximum allowed value of default correlation such that a portfolio composed of only two of these credits has a default probability of 0.2%?

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