For capital requirement, rwa is computed as a product of terms including a K (unexpected losses).

(As shown is the summary from wikipedia :



K is equal to (total loss - expected loss)×maturity adjustment.

Where maturity adjustment is defined as


I read some explanation for (total loss - expected loss) part that is coming the formula of a Merton conditional probability of dzfault. However I have no idea what is that formula for maturity adjustment. the b value (0.11852-0.05478ln(PD))^2 is also un-understood.

Is there any article proving these formulas, or explaining the rationale for their forms ? Their hard-coded values ?

Many thanks in advance


1 Answer 1


The maturity adjustment is there to take into account the risk of changing default probabilities in future years. Parameters are according to Basel calibrated from "observed... capital market data". It is covered in some detail in section 4.6 devoted to the subject in Basel's explainer on IRB riskweights.

  • $\begingroup$ Your document really helped. I guess the figures in b formula are voming from historical fitting. $\endgroup$
    – user25844
    Commented May 16, 2019 at 16:55
  • $\begingroup$ The b was calibrated to the output of the Credit portfolio models- Mark to market based models that take into account the transition matrices. $\endgroup$ Commented Sep 18, 2019 at 12:46
  • $\begingroup$ Also, the regulatory PD-limit is an input too. The adjustment does not work when PD approaches zero. $\endgroup$
    – Mats Lind
    Commented Sep 18, 2019 at 13:37

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