Basel-II Regulations(Servigny)

[Sunil Natarajan]

Hi David,
In Regulations chapter of De Servigny, it is mentioned under IRB approaches Probability of default(PD) is concave in shape i.e concave PD function.What does it mean?The LGD increases linearly with capital requirement(k).Does this apply in both IRB foundation and IRB advanced approaches.

Regards,
Sunil

 

[David Harper CFA FRM]

Hi Sunil,

I added a second tab to the IRB worksheet on this post (see 'concave PD' tab at bottom).
Or, here is worksheet directly: https://www.editgrid.com/bt/frm_2008/basel2_irb_v2
(on second tab bottom, is the concave PD)

It may be difficult to make sense of this without first engaging in the IRB formula. The LGD escapes the complex part of the formula, so it has linear impact on the captial charge. The PD, however, is weighted/blended into the copula-like formula with the N-1(99.9%) confidence, and this renders the capital charge as non-linear with PD. In pratical terms, this means higher levels of PD are not greatly impacting the charge.

The reason LGD is linear is that IRB uses downturn LGD consistenty: UL - EL both include the same 'downturn' LGD.
However, the PD is being translated into a conditional PD (the UL), so the IRB is basically: conditional PD * downturn LGD - PD* downturn LGD. If you want to be cynical, the PD is being abused for the sake of a convenient formula.

Yes, this applies regardless of (to both) foundation/advanced IRB. This has been a test question before: both IRB approaches must use this same formula, the difference is 'who gets to develop the inputs?'

For those interested, i just added a 3rd tab that shows the maturity adjustment in ADVANCED IRB (foundation assumes M = 2.5 years). Because it is *not* intuitive: higher PD has higher maturity adjustment. Yes, it's maybe weird PD is in the maturity. Yes, higher PD increases the adjustment. As de Servigny says, "higher quality facilities are more penalized by the maturity adjustment than low-quality ones."

David