afterworkguinness
Active Member
(I'm not 1,000% on this, so take it with a grain of salt. To my credit, I've read the relevant pages a couple hundred times over the year)
I was confused by usage of the single factor model presented in Malz (which by the way is called the Single Factor Vasicek Model - why some of the authors don't provide the names of the models they discuss I don't know)
He first says the model will solve for "conditional cumulative probability of default" - that's a contradiction in terms right ? A PD can either be cumulative where it expresses the PD over a period eg between year 1 and 5 (this is also called unconditional) or it can be conditional (also called marginal) where it's the PD at a certain time given no prior defaults eg PD of default at year 2 given no default thus far. But here Malz means the model is for a cumulative probability of default that is conditional upon the realization of a specific market factor.
A few pages later in the text, he shows that asset returns are assumed to be i.i.d and thus we can assume the law of large numbers and apply the single factor model to the entire portfolio as we would a single credit. He says we want the unconditional PD and will use it to solve for it. This sounds like a contradiction of his introduction to the model a few pages earlier but it's not. Let's look again at the definitions. Cumulative PD is another name for unconditional PD, recalling the conditional part described before wasn't conditional upon no prior defaults but conditional upon the market factor.
This confused me at first and really drove me nuts, so I hope this helps someone.
I was confused by usage of the single factor model presented in Malz (which by the way is called the Single Factor Vasicek Model - why some of the authors don't provide the names of the models they discuss I don't know)
He first says the model will solve for "conditional cumulative probability of default" - that's a contradiction in terms right ? A PD can either be cumulative where it expresses the PD over a period eg between year 1 and 5 (this is also called unconditional) or it can be conditional (also called marginal) where it's the PD at a certain time given no prior defaults eg PD of default at year 2 given no default thus far. But here Malz means the model is for a cumulative probability of default that is conditional upon the realization of a specific market factor.
A few pages later in the text, he shows that asset returns are assumed to be i.i.d and thus we can assume the law of large numbers and apply the single factor model to the entire portfolio as we would a single credit. He says we want the unconditional PD and will use it to solve for it. This sounds like a contradiction of his introduction to the model a few pages earlier but it's not. Let's look again at the definitions. Cumulative PD is another name for unconditional PD, recalling the conditional part described before wasn't conditional upon no prior defaults but conditional upon the market factor.
This confused me at first and really drove me nuts, so I hope this helps someone.
