Consider two firms,each of which has a distance-to-default of 1.The correlation of default of the two firms is $$\rho = 0.5$$ .Assuming bivariate normality,what is the probability that both firms default?
A)4.50%
B)6.25%
C)8.75%
D)10.25%

Question

Quizplus · Accepted Answer

The probability that both firms default, given a distance-to-default of 1 for each and a correlation of $\rho = 0.5$, can be found using the bivariate normal distribution. The distance-to-default of 1 corresponds to a default probability of approximately 15.87% for each firm individually (using the standard normal cumulative distribution function). Given the correlation of 0.5, the joint default probability is lower than the product of individual probabilities due to diversification effect. The correct calculation, often requiring numerical methods or tables specific to bivariate normal distributions, yields a probability of approximately 6.25%. This reflects the combined effect of individual default probabilities and the correlation between the firms' defaults.

Consider Two Firms,each of Which Has a Distance-To-Default of 1 ρ=0.5\rho = 0.5ρ=0.5

Consider Two Firms,each of Which Has a Distance-To-Default of 1 $\rho = 0.5$