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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 z-value 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(1-a(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 z-value 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 z-value 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(1-a(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 z-value 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