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Probability of Default (DP) and Default Event

A probability of default quantifies the chances of a borrower's default. Various definitions of default events could be used. They include a default of payment at due date, bankruptcy, or debt restructuring driven by a borrower's difficulties to face debt obligations. Basel 2 defines a default event as non-payment of debt obligations for 90 days.

A default probability refers to a period. The longer is the horizon, the higher are the chances of defaulting. Basel 2 imposes the usage of annualized default probability. Default probabilities depend on prevailing conditions, either general economic conditions or the firm's conditions. Under adverse economic conditions, chances of defaulting grow higher, and conversely. Basel 2 requires using "through-the-cycle" default probabilities, or probabilities that represent some average through the various phases of the economic cycle. Through-the-cycle probabilities of default can be higher or lower than "point-in-time" probabilities of default.

Basel 2 adopts a long-term prospective for defining chances of defaulting over a 1-year period, presumably for reducing pro-cyclicality of capital charge, which would otherwise be lower in expansion and higher in recession. Such sensitivity to economic conditions would require raising more capital in adverse conditions and reducing capital in favorable conditions, which is economically inefficient. Note that, in spite of such rules, many consider that Basel 2 capital remained pro-cyclical and one goal of the ongoing reforms of regulations is further smoothing capital requirements.

Normally, default probabilities should be related to credit ratings, but credit ratings are letter-grades ranking the credit risk, or ordinal measures. A default probability quantifies the risk (a cardinal measure). In retail activities, scoring techniques rely on numerous statistics which serve for quantifying default probabilities, based on historical data. For large corporations or banks, default statistics are not large enough to define default probabilities.

There is a variety of methodologies and data sources that banks may use to associate an estimate of DP to each of its internal grades. The three broad approaches are (i) use of data based on a bank's own default experience; (ii) mapping to external data; and (iii) use of statistical default models. Hence, a bank can use the foundation approaches as long as it maps, in a sound manner, its own assessment of ratings with default probabilities. A common practice, for "low-default-portfolios," relies on "mapping" of internal credit ratings to default frequencies based on historical data, mainly those of rating agencies. The approach has obvious drawbacks, one being that few corporations are rated and another that the bank's portfolio might not have the same composition as the portfolio of rated companies. The methodologies used for mapping credit scores and credit ratings to default probabilities are further discussed in Chapters 45 and 46. For corporate and bank exposures, the DP is the one-year DP associated with the internal borrower grade with a floor of 0.03%. For sovereign exposures, the DP is also associated with the sovereign risk grade, but the floor is zero.

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