Probability of default

The probability of failure ( often referred to as " PD ", of Engl. Probability of default) is, depending on the context, the probability of failure or malfunction of the system or a relationship and thus a statistical quantity. In the context of business administration can be broadly divided into the areas of technology and banking.

Technical failure probability

See Article: Failure rate

Probability of failure in banking

The probability of default or insolvency probability is the probability that a claim ( usually in the form of a loan but also of services and supplies ) fails, ie it is not paid (back). It affects the amount of the interest rates, because with it the expected loss to be covered out of business. Under Basel II stipulates that the capital that banks must deposit for loans of their probability of default depends ( Main article: minimum capital requirements for credit risk ).

Methods for estimating the probability of default

In general, two approaches are possible

• Debtors will vary depending on credit directly assigned to a rating class.
• From market data, which are dependent on the perception of the creditworthiness, the probability of failure is determined indirectly. This is possible because the rate or price of an investment object reflects the assessment of the market in terms of risk of the investment. For example, implies the higher interest rate of a bond X compared to an otherwise similarly equipped bond Y is a higher risk and therefore a higher probability of default of the bond X. If the interest rate for both bonds are equal, the higher the probability of default of the bond X about a lower price compared appears to bond Y.

Cumulative probability of failure

The cumulative failure probability is the probability that a loan for a certain period fails. Cumulative failure probabilities can be under the assumption that the one-year default probabilities over each period are equal, calculated using the following formula:

.

Here, the probability of default over a period of years and the one-year probability of default.

Example: The one-year default probability is 0.4%. The probability that the loan will default within the next five years is then

So approximately 1.98%.