# rationale for maturity adjustment formula in basel IRB formula

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

(1+(M-2.5)×b)/(1-1.5×b)

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 ?