Continuing the re-aging thread, a note circulated by APRA had a clear grip of the issue, and proposed:
“APRA’s proposed solution is to only allow the recording of a second default event after the loan has been in the non-default status for a period of at least 12 months”
‘Fraid I can’t give a direct reference as I only have an undated photocopy to hand, entitled “Multiple defaults in the retail portfolio” – it would have been about 2004. Please post to the blog any update on these issues that you may know of.
APRA’s concern was to “require the number of observations in bank’s PD and LGD databases to be equal” because of the traps of otherwise having mis-matched bases for PD and LGD. My preferred way of describing this – via “bad episodes” – is semantically different but hopefully faithful to the essence of the problem; it also lends itself to other difficulties that will be met.
Re-capping points from the last couple of posts:
- recognise that default definition starts with a point-in-time definition but also has a derived episodic dimension: every transition from good to bad at a point in time begins a bad episode which is a relatively long interval of time.
- the rule which specifies when the bad episode can end is an integral part of the default definition and is called the re-aging rule.
- these bad episodes will then be relatively few in number and will be the basic units of modelling
‘Relatively long’ and ‘Relatively few’ represent implicit recommendations to choose a re-aging rule that produces few, long, congealed bad episodes rather than the opposite. Technically, you could get out alive with a rule that makes many sporadic episodes but you will get a lot of unnecessary headaches: multiple non-independent episodes, large numbers of zero-loss LGD points, multiplicities within a year, and in general a dilution of modelling power through not aligning model constructs with a sensible grip on reality.
With this understanding, the APRA proposal says that the re-aging rule should allow a bad episode to end after 12 continuous non-bad months have elapsed. This seems a good choice and will produce well-congealed bad episodes. A particular merit is that two bad episodes for any particular account within any 12-month period is never possible. This is helpful because a lot of modelling (e.g. behavioural) has a 12-month OW and the chance of any multiplicity would be a nusiance.
Thinking in database terms, one would have only one source of default information: a table of default episodes, keyed by account and start date. Of course, bad episodes are well behaved constructs being distinct for any account and not overlapping. Depending how one implements the rule there can be a slight wobbly about whether a new episode can begin immediately that the previous one ends – imagine an account with B then 12G then B again – you decide how you like to treat this case – it’s not a showstopper.
For any longitudinal modelling, looking for the first default is equivalent to looking for the first start of a bad episode.
APRA’s concern that number of observations should be equal is trivially met because the table of default episodes is the common data source for either the PD modelling or the LGD modelling.
So does that solve everything? Not quite, just clears some problems so that we can face the more subtle ones standing in the shadows behind, AWML.
PS any corrections or updates on APRA or other regulatory opinions would be most welcome.