Gaussian copula modelling

[daweinzettl]

Dear All,

I am referring to the BIONIC Gaussian copula video on youtube. Can someone please explain (I need the formula and its derivation) how to get to the joint cumulative distribution function of 0.71 for two bonds with marginal cum. dist. function of 5% each and a correlation of 0.3?

Many thanks!

 

[David Harper CFA FRM]

hi @daweinzettl

We have a copula XLS in a learning spreadsheet, but Meissner has a (better) one associated with his new book http://www.amazon.com/dp/111879690X/?tag=bt077d-20 (FRM assigned) and I noticed that, as it should, his gives the same result of 0.71% for these assumptions.

Here is the his spreadsheet https://www.dropbox.com/s/ew3tipe4jh97kcv/2-asset_default_time_Copula.xlsm
It's a bivariate cumulative normal distribution and mine follows John Hull @ http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote5.pdf

I hope that helps

 

[daweinzettl]

David, I appreciate your answer, but I still do not know how the joint default prob. in your and Meissner's spreadsheet is derived. His spreadsheet "2-asset default time" contains a subroutine "bnc" and in the book ("Correlation Risk Modelling", page 81) there is no math or explanation about the formula of the subroutine.

 

[David Harper CFA FRM]

Hi @daweinzettl okay sure, understood. Here is my copula XLS @ https://www.dropbox.com/s/d0iinryts7cg89i/5.d.2.guassian_copula.xlsx Please note:

• For pr(x) = pr(y) = 5% and rho = 0.3, it returns the same joint PD of 0.7128%
• Mine does not employ the macro routines but rather implements Hull's technical note; i.e., I literally implemented this http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote5.pdf

I hope that helps, thanks,