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CDO models: Opening the black box – Part four
The Student-t copula
Loading the tails
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In the box “Copula Model Inputs” in addition to the Gaussian copula, the Student-t copula can be selected
As pointed out on slide 2, we assume that the marginal distribution is of the same kind as the joint distribution
Changing the copula alters the individual and joint behaviour of the pools constituents and therefore has a significant impact on the
risk/return characteristics of the portfolio as a whole but particularly for the individual tranches
Switching to the Student-t copula puts more weight on the tails, therefore spreads of junior tranches will be lowered, whereas fair spreads
for senior tranches will be significantly higher
On the following slides, we will analyse these risk/return characteristics and how they are altered when the copula is modified
We compare the standard Gaussian copula with the Student-t copula with 3 and 10 degrees of freedom (df)
For all three copula assumptions, we used the same parameters for the portfolio (5yrs, 100bps, 40% RR, 5% Interest rate) and correlation
(20%), together with 50,000 simulations
Copula Model Inputs
Simulation 10,000
Correlation 20.00%
Copula model Student-t 2
Student-t df 3
Dump loss distribution TRUE
Number of Bins 20
Select the Student-t
copula and specify the
number of degrees of
freedom.
Available Copula
(do not delete this area)
1
1 Normal
2 Student-t
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