Thread starter
#1
Hi David,
I am unclear on how deep we need to go to cover the GARP requirements on the Gaussian copula function (e.g. 505.3). Also, in trying to get some depth, I wanted to clarify this narrative. I am sure I have gaps in stringing it together.
In terms of building blocks, I have seen a single factor CDO model (i.e. the most basic form I think) can be used with variables representing market return ("m"), rho ("ai") i.e. correlation with (m)... and idiosyncratic risk, z(i). We saw a similar model in Part 1. With assumptions on risk free rate, recovery rate and market correlation (rho, m), this CDO model converts the single factor output x(i) into a zvalue and uses this to come up with a "market survival probability", from which we can solve (using the position's recovery rate), a time to default. This was the single factor model version I saw, but there are different flavors:
x(i) = sqrt(a(i))*m + sqrt(1a(i))*z(i)
The CDO goes on to be valued by creating a loss distribution based on the above, with a spread being calculated based on the simulated, present valued, loss adjusted value of the various names/ tranches.
In honesty, I am struggling to then tie this back to what I had read in the notes. Where for example is the portfolio correlation/ dependency coming from and the creation of the multivariate from marginals i.e. the copula magic? Perhaps I have misunderstood/ forgotten how the single factor model works and that the rho value (xi versus m) is actually the glue? And the zvalue equivalent of x(i) is the multivariate conversion process...?
Apologies this is a model and it is unfair to ask you to review it. Perhaps when I get to credit risk the picture will be become clearer... perhaps not (!) In any case I am struggling to understand the right pitch of knowledge on this complex topic. If you can advise.
Thanks
I am unclear on how deep we need to go to cover the GARP requirements on the Gaussian copula function (e.g. 505.3). Also, in trying to get some depth, I wanted to clarify this narrative. I am sure I have gaps in stringing it together.
In terms of building blocks, I have seen a single factor CDO model (i.e. the most basic form I think) can be used with variables representing market return ("m"), rho ("ai") i.e. correlation with (m)... and idiosyncratic risk, z(i). We saw a similar model in Part 1. With assumptions on risk free rate, recovery rate and market correlation (rho, m), this CDO model converts the single factor output x(i) into a zvalue and uses this to come up with a "market survival probability", from which we can solve (using the position's recovery rate), a time to default. This was the single factor model version I saw, but there are different flavors:
x(i) = sqrt(a(i))*m + sqrt(1a(i))*z(i)
The CDO goes on to be valued by creating a loss distribution based on the above, with a spread being calculated based on the simulated, present valued, loss adjusted value of the various names/ tranches.
In honesty, I am struggling to then tie this back to what I had read in the notes. Where for example is the portfolio correlation/ dependency coming from and the creation of the multivariate from marginals i.e. the copula magic? Perhaps I have misunderstood/ forgotten how the single factor model works and that the rho value (xi versus m) is actually the glue? And the zvalue equivalent of x(i) is the multivariate conversion process...?
Apologies this is a model and it is unfair to ask you to review it. Perhaps when I get to credit risk the picture will be become clearer... perhaps not (!) In any case I am struggling to understand the right pitch of knowledge on this complex topic. If you can advise.
Thanks
Attachments

473 KB Views: 16
Stay connected