Explanation:
Using the formula for the joint default probability (Φ ≡ π₁₂) derived from the default correlation:
Formula: Φ = ρ * π * (1 − π) + π²
Where:
Calculation: Φ = 0.45 * 0.0285 * (1 − 0.0285) + 0.0285² = 0.45 * 0.0285 * 0.9715 + 0.00081225 = 0.45 * 0.02768775 + 0.00081225 = 0.0124594875 + 0.00081225 = 0.0132717375 = 1.33%
Why other options are incorrect:
This calculation demonstrates how default correlation affects joint default probabilities in credit risk modeling.
Ultimate access to all questions.
The fixed-income trading desk of an investment bank uses several methodologies to estimate joint default probabilities of counterparties. The manager in charge of the desk asks an analyst to calculate the joint default probability of two firms (credits) over a 1-year period using the single-factor model. The portfolio consists of two firms (credits) that have the same beta to the market factor. The probability of default of each firm is 2.85%. If the analyst applies a default correlation between this pair of firms of 0.45, what is the joint default probability of the firms using the single-factor model?
A
1.25%
B
1.33%
C
2.65%
D
2.77%
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