Basel II Capital Adequacy: Internal Ratings-Based (IRB) Approach

The key cornerstone of prudential regulation of banks (and financial institutions in general) is to ensure that each bank holds sufficient equity capital to absorb unexpected losses, that is, the materialization of financial risks, principally market (price), liquidity, credit, and operational risks.
The so-called Basel II capital adequacy framework introduces a regulatory formula (Risk Weight Function, or RWF) that calculates how much minimum capital the bank must hold for each credit-risky asset, using the bank's own Probability of Default (PD) estimate for said credit-risky asset as the principal input. Because such PD estimates are generally based on the bank's internal credit rating system, this element of Basel II is referred to as the Internal Ratings-Based Approach (IRB).
The Basel II IRB-RWF thus codifies a greatly simplified credit portfolio model, whereby each individual asset's contribution to the portfolio credit risk is additive, homogeneous within each class of assets, and constructed by way of using a Gaussian copula to proxy dependency between credit defaults and the (dire/downturn) state of economy. The parametrization of this RWF is hard-coded, as per Basel Committee on Banking Supervision (BCBS), an international standard setting body based in Basel, Switzerland.
  • Contributed by: Poomjai Nacaskul
  • Quantitative Models & Financial Engineering, Bank of Thailand & MBA Program, Mahanakorn University of Technology


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Observe that the function is strictly concave and increasing as the probability of default (PD) is close to zero.
[1] Basel Committee on Banking Supervision. "International Convergence of Capital Measurement and Capital Standards." (June 2006) http://www.bis.org/publ/bcbs128.pdf.
[2] Basel Committee on Banking Supervision. "An Explanatory Note on the Basel II IRB Risk Weight Functions." (June 2005) http://www.bis.org/bcbs/irbriskweight.pdf.
[3] M. B. Gordy, "A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules," Journal of Financial Intermediation, 12(3), 2003 pp. 199–232.
[4] O. A. Vasicek, "The Loan Loss Distribution," Technical Report, KMV Corporation, 1997.


Contributed by: Poomjai Nacaskul
Quantitative Models & Financial Engineering, Bank of Thailand & MBA Program, Mahanakorn University of Technology
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+