CREDIT RISK MANAGEMENT: Based on a linear regression model, a bank calculates that the PD for one of its portfolio companies is -1%.

1.     
Based on a linear regression model, a bank calculates that the PD for one of its portfolio companies is -1%.

 

a.      
Interpret this PD and explain how it could have arisen.

b.     
How does the use of a logit model resolve any problems with the value of this PD?

c.      
What is the PD based on the logit model?

 

 

2.     
Using the KMV Model, you find that the assets (A) of a firm are $875 million, its debt (B) is $750 million, and the volatility of its assets (σA) is $53.6 million.

 

a.      
What is its distance to default?

b.     
Assuming a normal distribution, what is its probability of default?

 

3.     
Calculate the default probabilities in each of the two years using the following spot rates from the Treasury and corporate bond (pure discount) yield curves. Assume LGD = 50%.

 

1 Year             2 Year

Treasury bonds                                               5.0%                6.1%

BBB-rated bonds                                            7.0%                8.2%

 

 

 

4.     
A $100 million BBB loan has 3 possible credit migrations over the next year:

 

Probability                   Value

AAA                           15%                             $110 million

BBB                            84.5%                          $100 million

D                                 0.5%                            $50 million

 

a.      
What is the fair market price of the loan?

b.     
What is the loan’s capital requirement at the 99% level using the normal distribution?

c.      
What is the capital requirement using the actual distribution?