Financial Risk Manager Part 2

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Explanation:

Let:
D₁ = probability of default by firm 1 and
D₂ = probability of default by firm 2
ρ₁₂ = correlation of defaults

The Joint probability of default is given by:

P(D_1 D_2) = D_1 \times D_2 + \rho_{12} \times \sqrt{D_1(1 - D_1)} \sqrt{D_2(1 - D_2)}

Since the defaults are correlated,

P(D_1 D_2) = 5\% \times 1\% + 0.2 \times \sqrt{5\%(1 - 5\%)} \sqrt{1\%(1 - 1\%)} \approx 0.484\%

N/B: If the defaults were uncorrelated,
i.e., ρ₁₂ = 0

P(D_1 D_2) = 5\% \times 1\% = 0.05\%

This means that the joint probability of default for correlated defaults is nearly 10 times higher than the one for uncorrelated defaults.

Explanation:

Let:
D₁ = probability of default by firm 1 and
D₂ = probability of default by firm 2
ρ₁₂ = correlation of defaults

The Joint probability of default is given by:

P(D_1 D_2) = D_1 \times D_2 + \rho_{12} \times \sqrt{D_1(1 - D_1)} \sqrt{D_2(1 - D_2)}

Since the defaults are correlated,

P(D_1 D_2) = 5\% \times 1\% + 0.2 \times \sqrt{5\%(1 - 5\%)} \sqrt{1\%(1 - 1\%)} \approx 0.484\%

N/B: If the defaults were uncorrelated,
i.e., ρ₁₂ = 0

P(D_1 D_2) = 5\% \times 1\% = 0.05\%

This means that the joint probability of default for correlated defaults is nearly 10 times higher than the one for uncorrelated defaults.

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Last updated: July 5, 2026 at 07:27

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