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Explanation:

Joint default probability is given by the formula:

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

Given $\pi_1$ and $\pi_2$ are equal, it implies that $\pi_1 = \pi_2 = \pi$

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

\pi_{12} = \rho_{12} \times \pi(1 - \pi) + \pi^2

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Q.1833 A pair of credits with BBA- and BBA+ ratings has equal default probabilities. If $ \rho_{12} $ is the default correlation between them, find an appropriate expression for the joint default probability. | Financial Risk Manager Part 2 Quiz - LeetQuiz

Financial Risk Manager Part 2

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Q.1833 A pair of credits with BBA- and BBA+ ratings has equal default probabilities. If ρ12\rho_{12}ρ12​ is the default correlation between them, find an appropriate expression for the joint default probability.

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Q.1833 A pair of credits with BBA- and BBA+ ratings has equal default probabilities. If $\rho_{12}$ is the default correlation between them, find an appropriate expression for the joint default probability.