Asset & default correlation (Malz, Portfolio Credit Risk chapter)

[daweinzettl]

Hi all,


just one question on using the numerical procedure to solve for the asset correlation (ß^2) in Malz, page 281.


Can someone please show how to solve for beta and the joint default prob. given the investment grade default prob. (0.01) and the default correlation (0.05) ? ß^2 should be 0.315 and the joint default prob. amounts to 6bp.


any input is highly appreciated!

 

[ShaktiRathore]

Let x be joint default pribabiluty,pd of other bond be y
.05=x-.01*y/sqrt(.01*.99)*sqrt(y(1-y))
x=.0006
.05*.0995*sqrt(y(1-y)=.0006-.01y
.000024*y(1-y)=.00000036+.0001y^2-.000012y
24y(1-y)=.36+100y^2-12y
124y^2-36y=.36 ignore .36,y=36/124=.29
Ccheck for beta^2 by putting these values. Such questions can be cross checked by putting values given in the equation and check whether they satisfy the equation. Go this way u think u shall get the answer.
Hope this helps
Thanks

 

[daweinzettl]

many thanks for your comment. I can follow your steps till the last line, but I don't quite understand what you did in the last line? Why do you ignore 0.36? Your result for "y" is 0.29, but how do I get the default correlation (ß^2) of 0.315?

We don't know the joint def. prob. (x= 0.006) in advance.

 

[ShaktiRathore]

Hi
I ignore .36 just to simplify calculations. Otherwise as i calculated the exact answer for y is .3.
What is your source of the question, can you please give complete details of the problem, where u get it from?please elaborate
Thanks

 

[daweinzettl]

Hi,

the source is "Fin. Risk Management" by Malz, Chapter 8 (Portfolio Credit Risk), page 281. I have uploaded the page in Malz' book I'm referring to.

 

[daweinzettl]

here is the previous page (280) as well, in the case you don't have the book ready. Thank you!

 

[daweinzettl]

David, may we ask for your comment please?

 

[afterworkguinness]

HI @ShaktiRathore , can you walk me through your steps? Thanks