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 $\operatorname { Pr } \left[ D _ { 1 } \mid D _ { 2 } \right]$ ?

If a firm has a distance-to-default of 2,and we assume a normal distribution,then the probability of a firm defaulting is

Which of the following isnot a reason to favor the top-down approach to modeling correlated default versus the bottom-up approach?

You are assessing a credit portfolio with 100 issuers where the hazard rate of default of each name is 0.05.The default correlation of all firms (pairwise)is zero.What is the average time it will take for 10% of the portfolio to default?

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?

If you expect default correlations to increase in the future,what trade might you engage in to profit from this view?

A self-exciting model for defaults is one where

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 these two firms is $\rho = 0.30$ .What is the price of a $100 notional one-year maturity first-to-default basket option on these two firms? (Assume the discount rate is zero. )

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 $\operatorname { Pr } \left[ D _ { 2 } \mid D _ { 1 } \right]$ ?

Which of the following is an Archimedean copula over two distribution functions

A second-to-default (STD)basket option pays off when any one of the companies in a credit basket defaults.The price of the STD basket increases when

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?

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 probability of a second-to-default basket option that pays $100 if any both firms default within a year? (Assume zero discount rates. )

In the Longstaff and Rajan top-down correlated default model,assume that losses $L _ { t }$ in a credit portfolio are given by the following dynamic process in a one-factor setting: $\frac { d L _ { t } } { 1 - L _ { t } } = \gamma d N ( \lambda )$ where $\gamma$ is a fractional loss (of the current portfolio value)that occurs every time there is a default,assumed to be generated by a Poisson process $N$ with loss arrival rate $\lambda$ (a constant).What is the expected loss of a $100 portfolio in a year if $\gamma = 0.01$ and $\lambda = 2$ ?

A CDO has three tranches,a senior tranche,mezzanine tranche,and equity tranche.Keeping the probabilities of default in the CDO collateral fixed,the value of the equity tranche increases if

The difference between implied correlation and base correlation in CDOs is that

Two firms that have zero default correlation and expected losses conditional on default of $2 million and $3 million,respectively.The probability of loss of the two firms in one year is 0.10 and 0.05,respectively.What is the mean loss of this portfolio?

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 these two firms is $\rho = 0.30$ .What is the price of a $100 notional one-year maturity second-to-default basket option on these two firms? (Assume the discount rate is zero. )

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 probability of a first-to-default basket option that pays $100 if any one firm defaults within a year? (Assume zero discount rates. )