Exam 32: Modeling Correlated Default

Consider two firms with one-year probabilities of default of $p _ { 1 } = 0.10$ and $p _ { 2 } = 0.05$ , respectively. The correlation of default of the two firms is $\rho = 0.5$ . What is the conditional probability of default $\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right]$ ?

Consider two firms, each of which has a distance-to-default of 2. The correlation of default of the two firms is $\rho = 0.5$ . Assuming bivariate normality, what is the value of a $100 notional first-to-default basket option on these two firms, if the discount rate is zero?

Which of the following isnot an important benefit of using copula functions for correlated default?

Consider two firms with one-year probabilities of default of $p _ { 1 } = 0.10$ and $p _ { 2 } = 0.05$ , respectively. The conditional probability of default in one year is $\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right] = 0.7$ . What is the correlation of default of these two firms closest to?