Probability of failure

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The probability of default (PD Abbreviation of English Probability of Default ) is the banking system , a banking supervisory legal risk parameters for the measurement of credit risk .


In addition to the probability of default, there are also the default loan amount (EaD) and the default loss rate (LGD) as risk parameters . These parameters were first introduced in January 2007 in all EU member states , in Germany through the Solvency Regulation . Its supervisory function has been taken over by the Capital Adequacy Regulation (CRR), which also applies in all EU member states, since January 2014 . It provides legal definitions for these parameters . All three parameters are hypothetical quantities that are based on stochastic probabilities .


In Article 4, Paragraph 1, No. 54, the Capital Adequacy Ordinance defines the probability of default as the “probability of a counterparty defaulting over the course of a year”. The term counterparty is broadly defined and includes any natural or legal person who conducts banking transactions with a bank and for whom the bank has examined the creditworthiness (Art. 286 (2a) CRR). According to Art. 178 CRR, default is considered to have been given if it is unlikely that the debtor will settle his liabilities in full or a material liability of the debtor is more than 90 days overdue.

The probability of default is assigned to the borrower level, since it is not a single claim but a debtor with all claims that defaults. All balance sheet risk positions of money lending ( credit business ) and off-balance sheet business of credit lending ( guarantee credits , letters of credit , derivatives ) vis-à-vis a borrower unit must therefore be recorded .

The estimate is based on the bank's internal or external past data on credit defaults that have occurred with at least 5 years of observation, which are condensed into a graduated default frequency and can then be assigned ( calibrated ) to each individual rating level . The institutions estimate the probability of default for the individual rating levels based on the long-term averages of the annual default rates (Art. 180 Para. 1a CRR). This gives the best rating level the lowest probability of default and the worst rating the highest. Here, future rating migrations of each borrower must be taken into account as part of a recalibration. According to the empirical default studies by the rating agency Standard & Poor’s , there is a clear positive correlation between credit risk and the probability of default, because the better the rating , the lower the probability of default and vice versa.


Credit institutions that choose the credit risk standard approach for rating are given the default probability by the banking supervisory authority as a default value. All other institutions that use the IRB foundation approach or the advanced IRB approach determine the probability of default themselves.

Art. 160 para. 1 CRR specifies the extreme values, so that the default probability of companies ( non-banks ) and credit institutions to be applied must be at least 0.03%, while the default probability of defaulted debtors according to Art. 160 para. 3 CRR is 100% got to. When determining the probability of default, personal security may be taken into account (Art. 160 Para. 4 CRR). Banks that use the advanced IRB approach may also take property collateral into account (Art. 160 (5) CRR).

The cumulative probability of default is the probability that a loan will default over a period of time. Cumulative default probabilities can be calculated with the assumption that the one-year default probabilities are the same over every period using the following formula:

It is the probability of default over a period of years and the one-year probability of default.

If the one-year probability of default is 0.4%, the probability is that the loan will default within the next five years


so about 1.98%.


It is only when the rating levels are calibrated through graduated probabilities of default that the rating becomes of economic importance through differentiation of creditworthiness . As soon as the lender has determined the probability of default, the behavior of risk compensation , risk standardization and risk avoidance is available to him . The default probability, graded according to rating class, results in a different grading of the credit margin and thus the loan interest for each rating class as part of the risk compensation . The higher the probability of default, the higher the loan interest and vice versa. The terms and conditions used by credit institutions are therefore largely based on the probability of default. The lending business can then be controlled through differentiated loan interest rates, because low interest rates are only offered with good credit ratings, while high interest rates are less attractive for poor credit ratings. The risk standardization ensures that a certain credit risk is not exceeded, so that if the risk is avoided, a credit decision below the investment grade is negative.


The technical failure probability is treated in the failure rate .

See also

Individual evidence

  1. Henner Schierenbeck : Earnings-Oriented Bank Management , Volume 1, 2001, p. 319.
  2. Marcus Riekeberg: Credit pricing for corporate customers, taking into account creditworthiness migration and credit value at risk values . In: Bank-Archiv Wien 50, 2002, pp. 457 ff.
  3. Standard & Poor's (Ed.): Default, Transition, and Recovery: 2007 Annual Global Corporate Default Study and Rating Transitions , 2008, p. 10.
  4. Andreas Pfingsten: Credit services: Die Kreditvergabe , in: Georg Obst, Otto Hintner: Geld-, Bank- und Börsenwesen, 2000, p. 688.
  5. Marc-Oliver Obermann, Balance Sheet Policy and Lending Decisions, 2011, p. 75