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

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.

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UAnonymous

Last updated: July 5, 2026 at 07:14

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

$\pi_{12} = \rho_{12}$

$\pi_{12} = \pi_1^2$

$\pi_{12} = \pi^3$

Financial Risk Manager Part 2