Question 1

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

Accepted Answer

A)  The loss distribution in simple cases is easy to compute in closed-form. 
B)  The computational complexity of the top-down approach is far less than that of the bottom-up one. 
C)  It is easier to model CDOs on CDOs. 
D)  It enables breaking down the portfolio loss name by name. 
A)  The loss distribution in simple cases is easy to compute in closed-form. 
B)  The computational complexity of the top-down approach is far less than that of the bottom-up one. 
C)  It is easier to model CDOs on CDOs. 
D)  It enables breaking down the portfolio loss name by name. D

Question 2

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?

Accepted Answer

A)  $250,000 
B)  $350,000 
C)  $400,000 
D)  $500,000 
A)  $250,000 
B)  $350,000 
C)  $400,000 
D)  $500,000 B

Question 3

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

Accepted Answer

A)  1.1% 
B)  1.5% 
C)  2.1% 
D)  2.3% 
A)  1.1% 
B)  1.5% 
C)  2.1% 
D)  2.3% D

Question 4

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

Accepted Answer

A)  0.38 
B)  0.42 
C)  0.46 
D)  0.50 
A)  0.38 
B)  0.42 
C)  0.46 
D)  0.50

Question 5

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?

Accepted Answer

A)  1/5 year 
B)  1/2 year 
C)  1 year 
D)  2 years 
A)  1/5 year 
B)  1/2 year 
C)  1 year 
D)  2 years

Question 6

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.)

Accepted Answer

A)  $0.50 
B)  $1.50 
C)  $2.50 
D)  $3.50 
A)  $0.50 
B)  $1.50 
C)  $2.50 
D)  $3.50

Question 7

Consider two firms with hazard rates $\lambda _ { 1 } = 0.10$ and $\lambda _ { 2 } = 0.05$ . The correlation of their default times is zero. What is the approximate probability that both firms default within five years?

Accepted Answer

A)  5% 
B)  9% 
C)  13% 
D)  17% 
A)  5% 
B)  9% 
C)  13% 
D)  17%

Question 8

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

Accepted Answer

A)  Buy the senior tranche of a CDO. 
B)  Buy a second-to-default basket option and sell a first-to-default basket. 
C)  Sell a second-to-default basket option and buy a first-to-default basket. 
D)  Short the equity tranche of a CDO. 
A)  Buy the senior tranche of a CDO. 
B)  Buy a second-to-default basket option and sell a first-to-default basket. 
C)  Sell a second-to-default basket option and buy a first-to-default basket. 
D)  Short the equity tranche of a CDO.

Question 9

Which of the following is an Archimedean copula over two distribution functions $F _ { 1 } , F _ { 2 }$ ?

Accepted Answer

A)  $C \left( F _ { 1 } , F _ { 2 } \right) = \ln \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$ 
B)  $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { a } \right\}$ 
C)  $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$ 
D)  None of the above. 
A)  $C \left( F _ { 1 } , F _ { 2 } \right) = \ln \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$ 
B)  $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { a } \right\}$ 
C)  $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$ 
D)  None of the above.

Question 10

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

Accepted Answer

A)  The correlation of default across all names in the CDO increases. 
B)  The correlation of default across all names in the CDO decreases. 
C)  The credit quality of names in the CDO collateral declines. 
D)  The volatility of credit spreads on names in the CDO collateral increases. 
A)  The correlation of default across all names in the CDO increases. 
B)  The correlation of default across all names in the CDO decreases. 
C)  The credit quality of names in the CDO collateral declines. 
D)  The volatility of credit spreads on names in the CDO collateral increases.

Question 11

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.)

Accepted Answer

A)  $10.00 
B)  $12.50 
C)  $15.00 
D)  $17.50 
A)  $10.00 
B)  $12.50 
C)  $15.00 
D)  $17.50

Question 12

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 probability that both firms default in one year?

Accepted Answer

A)  1.0% 
B)  1.5% 
C)  2.0$ 
D)  2.5% 
A)  1.0% 
B)  1.5% 
C)  2.0$ 
D)  2.5%

Question 13

The value of a CDO (collateralized debt obligation) unambiguously increases when

Accepted Answer

A)  The correlation of default amongst the names in the CDO decreases. 
B)  The correlation of default amongst the names in the CDO increases. 
C)  The intensity of default of names in the portfolio decreases. 
D)  The number of names in the CDO decreases. 
A)  The correlation of default amongst the names in the CDO decreases. 
B)  The correlation of default amongst the names in the CDO increases. 
C)  The intensity of default of names in the portfolio decreases. 
D)  The number of names in the CDO decreases.

Question 14

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?

Accepted Answer

A)  4.50% 
B)  6.25% 
C)  8.75% 
D)  10.25% 
A)  4.50% 
B)  6.25% 
C)  8.75% 
D)  10.25%

Question 15

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.)

Accepted Answer

A)  $10.00 
B)  $11.50 
C)  $14.25 
D)  $17.35 
A)  $10.00 
B)  $11.50 
C)  $14.25 
D)  $17.35

Question 16

In the Longstaff and Rajan top-down correlated default model, assume that losses  $L _ { 4 }$ 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 $\lambda = 2$ ?

Accepted Answer

A)  $1.5 
B)  $2.0 
C)  $2.5 
D)  $3.0 
A)  $1.5 
B)  $2.0 
C)  $2.5 
D)  $3.0

Question 17

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

Accepted Answer

A)  Base correlation is the smallest correlation implied across all tranches of a CDO. 
B)  Base correlation is the correlation of cumulative sets of tranches starting with the equity tranche, whereas implied correlation is for single tranches only. 
C)  All base correlations are implied, but not all implied correlations are base correlations. 
D)  Base correlation is historical and implied correlation is computed using tranche prices at a point in time. 
A)  Base correlation is the smallest correlation implied across all tranches of a CDO. 
B)  Base correlation is the correlation of cumulative sets of tranches starting with the equity tranche, whereas implied correlation is for single tranches only. 
C)  All base correlations are implied, but not all implied correlations are base correlations. 
D)  Base correlation is historical and implied correlation is computed using tranche prices at a point in time.

Question 18

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

Accepted Answer

A)  The credit quality of any issuer in the basket improves. 
B)  The correlation of default across names in the basket increases. 
C)  The correlation of default across names in the basket decreases. 
D)  The volatility of credit spreads for names in the basket decreases. 
A)  The credit quality of any issuer in the basket improves. 
B)  The correlation of default across names in the basket increases. 
C)  The correlation of default across names in the basket decreases. 
D)  The volatility of credit spreads for names in the basket decreases.

Question 19

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.)

Accepted Answer

A)  $2.50 
B)  $5.50 
C)  $11.25 
D)  $17.75 
A)  $2.50 
B)  $5.50 
C)  $11.25 
D)  $17.75

Question 20

A self-exciting model for defaults is one where

Accepted Answer

A)  There are non-random exogenous changes in the rate at which defaults arrive. 
B)  The volatility of the intensity increases with the level of losses. 
C)  The rate at which defaults arrive increases with the level of losses. 
D)  Excitement from defaults is spontaneous! 
A)  There are non-random exogenous changes in the rate at which defaults arrive. 
B)  The volatility of the intensity increases with the level of losses. 
C)  The rate at which defaults arrive increases with the level of losses. 
D)  Excitement from defaults is spontaneous!

Exam 32: Modeling Correlated Default

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

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?

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

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 with hazard rates λ1=0.10\lambda _ { 1 } = 0.10λ1​=0.10 and λ2=0.05\lambda _ { 2 } = 0.05λ2​=0.05 . The correlation of their default times is zero. What is the approximate probability that both firms default within five years?

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

Which of the following is an Archimedean copula over two distribution functions F1,F2F _ { 1 } , F _ { 2 }F1​,F2​ ?

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

Consider two firms with one-year probabilities of default of p1=0.10p _ { 1 } = 0.10p1​=0.10 and p2=0.05p _ { 2 } = 0.05p2​=0.05 , respectively. The correlation of default of these two firms is ρ=0.30\rho = 0.30ρ=0.30 . What is the probability that both firms default in one year?

The value of a CDO (collateralized debt obligation) unambiguously increases when

Consider two firms, each of which has a distance-to-default of 1. The correlation of default of the two firms is ρ=0.5\rho = 0.5ρ=0.5 . Assuming bivariate normality, what is the probability that both firms default?

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

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

A self-exciting model for defaults is one where

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Consider two firms with hazard rates $\lambda _ { 1 } = 0.10$ and $\lambda _ { 2 } = 0.05$ . The correlation of their default times is zero. What is the approximate probability that both firms default within five years?

Which of the following is an Archimedean copula over two distribution functions $F _ { 1 } , F _ { 2 }$ ?

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 probability that both firms default in one year?

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?