These typologies overlap but 57.2-3 trumps 56.5. The curriculum is weak here, frankly. Garp made a mistake with 56.5; it refers to an unassigned reading (Gallatti, chapter 4), of which I notified GARP earlier in the year.
LO 57.x are relevant, for our purposes. The four in 56.5 roughly map to them, anyway but why confuse; i.e., economic pricing maps to top-down multi-factor/income-based and the other three roughly map to bottom-up approaches.
I'd say the categories in 56.5 are not relevant although you'll notice the advantages/disadvantages of bottom-up are helpful and are important: bottom-up is forward-looking; bottom-up distinguishes between HFLS & LFHS; bottom-up tends to be either people and process-intensive or data intensive. A real shortcut view: bottom up tends to be predicatively superior but more people/data intensive. The advanced approaches are bottom up.
So, in regard to approaches to operational risk, I'd focus on 57.2 & 57.3 and ignore 56.5. The other 'typology' we can care about is the Basel II AMA. Note its mappings to the 57.x:
basic indicator: top down, income-based
standardized: also top down, income-based
AMA #1: IMA
AMA #2: loss distribution
AMA #3: Scorecard
So, that AMA has the typology I find most useful. You've got two quant approaches and one qualitative (or "process oriented") approach (scorecard). And the quants divide into a risk indicator approach (IMA) or frequency/severity distributions (loss distribution)
That's interesting. I think some critics of Basel II would say it achieves neither. But, aspirationally, Basel wants both. There are two aspects to this (measurement vs. management) that are relevant, to the FRM candidate, that I can think of:
1. LO 68.15: Discuss the â€œevolutionary aspectâ€ of the risk measurement procedures addressed in the Basel II Accord.
This evolutionary aspect might be viewing in context of measurement versus management, for all risks (market, credit) including operational risk. The "price" of the advanced approach (AMA) is that the bank must satisfy an additional set of quantitative/qualitative standards; most of these relate to evidence of a robust risk management system. So, the evolution, as the bank moves from BIA to SA to AMA, is to (presumably) lower capital charges with more advanced methods but conditional on better management systems.
2. The second Pillar. The first pillar is measures. The OpRisk methods above, at the "lower" end are merely measures (% of operating income). As you move into bottom-up methods, those are measures too but arguably start to blend into risk management; e.g., when you start to map out process and causal chains, you are working to manage (prevent).
But still, the first pillar shows how to produce measures (capital charges). If you look at the four principles of the second pillar, they are all about giving regulators the license to monitor risk management systems. That's why Jorion (I think) calls it the important going forward, "load bearing" pillar: the first is measurement compliance but the second aspires to encourage good risk management practice.