I wish to find the the implied conditional probablity of default from CDS spreads. I have already used the O'Kane/Turnbull Lehman brothers paperto find the implied unconditional probability of default from CDS spreads. Now I would like to use these probabilities to construct the implied conditional probability of default of entity A defaulting conditional on the PD of entity B.
The way I did this initially was via constructing the joint PD of A and B via a Gaussian copula and dividing by the marginal PD of entity B.
To do this the method is:
1. Construct correlation matrix, say a 2x2 with the correlation of the PD's off the diagonal and 1's on the diagonal.
2. Wrote some code for Cholesky decomposition. A simple function in VBA, if you are stuck here there are examples on the net.
3. Multiplied the Normsinv(PDA) and Normsinv(PDB) with the resulting Cholesky matrix and took the normsdist.
i.e. normsdist(normsinv(PDA)*? + nomrsinv(PDB) * sqrt(1-?^2))
This should be the joint probability distribution, right?
y problem is that the joint probability distribution is higher than the marginals. Does anyone have any idea of where I go wrong?
The way I did this initially was via constructing the joint PD of A and B via a Gaussian copula and dividing by the marginal PD of entity B.
To do this the method is:
1. Construct correlation matrix, say a 2x2 with the correlation of the PD's off the diagonal and 1's on the diagonal.
2. Wrote some code for Cholesky decomposition. A simple function in VBA, if you are stuck here there are examples on the net.
3. Multiplied the Normsinv(PDA) and Normsinv(PDB) with the resulting Cholesky matrix and took the normsdist.
i.e. normsdist(normsinv(PDA)*? + nomrsinv(PDB) * sqrt(1-?^2))
This should be the joint probability distribution, right?
y problem is that the joint probability distribution is higher than the marginals. Does anyone have any idea of where I go wrong?
