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Default risk is the probability of the event of default. Several events qualify as default, which we review. Migrations are either deteriorations or improvements of the credit standing of obligors, which translate, respectively, into higher or lower default probabilities. For default events, losses are readily observable. For migrations, the valuation of risk necessitates a mark-to-market valuation.

Definitions of Default

There are several possible definitions of default: missing a payment obligation for a few days, missing a payment obligation for more than 90 days, filing for bankruptcy, restructuring imposed by lenders, breaking a covenant triggering a cross-default for all lenders to the same entity. It depends on default definition.

A payment delay of a few days for individuals or small businesses is closer to delinquency than default, to the extent that the likelihood of getting the payment remains high. Payment default commonly refers to a minimum period, such as 3 months after due date. Bankruptcy and restructuring are default events, since they follow major failure of payment obligations.

Covenants trigger default events. Nevertheless, there is a wide spectrum of covenants. Many trigger a technical default, requiring a waiver from lenders before continuing operations. Such events usually initiate negotiation, whatever the risk to the borrowers survival. Some covenants trigger cross-default and cross-acceleration. Cross-default implies that a failure of payment with respect to any debt obligation of the lender triggers a default for all lenders. Cross-acceleration specifies that prompt repayments are due immediately, although this might only result in prompt renegotiation with all lenders. Still, without waivers granted by lenders, the borrower becomes bankrupt.

Another view on default is economic. It occurs when the value of the assets of the borrower dips below the value of the debt. This is economic default under the Merton (1974) model, implemented in instrumental default models such as KMV Credit Monitor.

The definition of default is critical for estimating default probabilities and measuring historical default frequencies. Rating agencies usually consider that default occurs when missing a contractual payment. The New Basel Accord includes bankruptcy and restructuring as default events, and makes it necessary to build up histories of such events as well. Economic default differs from legal or conventional default rules, but serves for modelling default.

Finally, securitization structures and funds default when a breach of covenant occurs. The loss under default is more difficult to define than for a loan because default events of structures trigger early amortizations of the notes held by lenders with the amortization of the pool of assets securitized or through liquidation.

Default and Migration Probabilities

The probability that default occurs during a given period characterizes default risk. The probability that a firm migrates from one risk class to any other is a migration. Default is one of these migration states, except that it is an absorbing state.

Under default, the loss materializes and is the amount at risk less recovery. Valuing migrations is different. The migration probabilities result from historical data. Nevertheless, a migration to any state other than the default state does not trigger any loss in book value, although the default probability changes. Marking-to-market transactions value the change in credit quality because it discounts future flows at rates that depend on credit spreads, and credit spreads vary across credit states.

Historical data provide default frequencies according to a specific definition of defaults. Rating agencies provide historical frequencies of defaults of payments exceeding 90 days. Some central banks have default histories of both missed payments and bankruptcies. The drawback of such historical data is that they do not capture expected default rates. The next chapter provides an overview of historical data on defaults and recoveries using rating agencies data.

A common practice is to map default frequencies with agency ratings. However, a rating is not a direct measure of a default probability of an issuer. Agencies rate the quality of risk of a debt issue, rather than the credit standing of the issuer, defined as the severity of losses, which depends on both default probability and recoveries under default. Therefore, ratings of issues in general do not correspond exactly to issuers ratings and their default probabilities. Nevertheless, they do correlate with historical default frequencies. In practice, banks often assign internal ratings (see Chapter 35) and map them with agency ratings in order to map their own ratings with default frequencies.

This is the route proposed by the Internal Ratings-Based (IRB) approach of the New Basel Accord. The alternative route is to model directly default events, such as KMV Credit Monitor or Moodys RiskCalc.

Several chapters deal with default and migration risk. One provides an overview of the historical data. Another deals with all the techniques for modelling default probabilities or ratings, using statistical techniques, such as RiskCalc and others. A chapter is dedicated to the option view on default used by KMV Credit Monitor.