## BLOCK I: STANDALONE RISK

Category: Risk Management in Banking

This block discusses risk drivers, exposure and credit risk valuation. The credit risk drivers are the factors that trigger credit risk events, default or migrations across risk classes. The exposures to credit risk use either actual or expected exposures, or modelled exposures such as those of over-the-counter derivatives, which are market-driven. Credit valuation implies calculating value changes due to credit events. Under default mode, values do not reflect risk migrations. Under full valuation mode, migrations drive value changes.

**Modelling Default and Migration Risks**

Default and migration probabilities are basic inputs for capturing the risk of a facility as well as the risk of a portfolio. The New Basel Accord considers that assigning default probabilities to borrowers is a requirement for implementing the foundation and advanced approaches, rather than the standardized approach. When implementing portfolio models, it is necessary to specify exposure, recoveries (or loss given default) and the likelihood of default and migrations. This is an area where old scoring and rating models, capable of mimicking the ratings assigned by agencies from observable firms attributes, and new models capable of modelling default probabilities directly with other techniques coexist. Both old generation models and new generation models have expanded at a fast pace since the full recognition of the necessity of ratings and default probabilities by the regulatory authorities in Basel.

**Assigning Ratings and Default Probabilities: Judgmental versus Analytical**

Ratings rank the credit risk of debt issues. When assigning ratings, there are various dimensions of the risk of a loan to capture. The first is the risk of the borrower. This is a counterparty risk, rather than a facility risk. The facility risk depends on collateral, third-party guarantees and informal support of a holding company. A comprehensive rating scheme should capture the effect of the borrowers risk, a possible supporting entity effect, plus the facility-specific guarantees mitigating effects. Traditionally, external ratings from agencies qualify the risk of issues, the equivalent of facilities within a bank. Several issues from the same borrower have different ratings depending on their seniority level and their secured-unsecured status. The need for issuer, or borrower, ratings became more important because default probabilities are critical inputs, as are recoveries.

The most common way to assign default probabilities to facilities is through the internal rating system of the bank. This is the Internal Ratings-Based (IRB) approach of the New Basel Accord. The forthcoming regulations on credit risk require these internal ratings to better capture risk differentiation than the former Cooke ratio. First from internal ratings to external ratings of rating agencies, and second from these to the historical default frequencies, as recorded historically by agencies for the portfolio of rated entities. Using this double mapping assumes that such portfolios are representative of banks portfolios, which is not the case in general. For instance, many rated entities are very large companies, while banks borrowers are not.

The alternative route is to use models to generate internal ratings or default probabilities. When modelling ratings only, the mapping procedure above is again necessary to convert ratings into default probabilities. The difference with a standard internal rating system is the usage of a model to assign the rating, eventually modified by credit officers. The direct modelling of the default probability has existed for a long time. It is currently moving ahead under the incentives of regulators to generalize the usage of default probabilities within banks. There are various ways to reach this stage, with old and new generations of default risk models. Note that KMV is the only firm using a default probability model for listed firms and a portfolio model using the same conceptual framework.

**Ratings and Default Models**

In general, ratings depend on a number of factors, as explained in Chapter 35. Rating models try to replicate actual ratings using a function of some quantitative financial ratios plus, eventually, other qualitative variables. They use a wide spectrum of techniques, ranging from multivariate statistical analyses, regression analyses, to more elaborate logit-probit techniques, and up to neural network models. Rating models, however, do not suffice for portfolio risk modelling since it remains necessary to transform ratings into default probabilities.

Rather than modelling ratings, default models attempt to predict the default frequency. The main differences are:

• Default events are objective, whereas ratings are somewhat judgmental.

• Modelling directly default events does not require any conventional mapping of ratings to default probabilities.

• Default models provide directly the necessary inputs for portfolio models.

• Nevertheless, a default model requires databases on defaults to fit the models, which is an important difficulty given the relative scarcity of data on defaults and default sources.

Note that default models and rating models use symmetric processes. With rating models, we assign a rating and, through a mapping of ratings with default probabilities, we infer what the default probabilities are. With default models, we model directly the default probability, and then we infer the rating through mapping default probabilities with any rating scale. Default models have extended the range of techniques, using the now famous option model of default, originally presented by Merton (1974), and later made popular by KMV Credit Monitor, as explained below.

**Techniques for Modelling Ratings and Default Probabilities**

Various techniques apply to the modelling of ratings and of default probabilities, some of them being fairly old and others very recent.

The simple multivariate linear regression provides valuable fits between financial attributes and ratings, and it can extend to qualitative variables as well. This is a good starting point. More elaborated techniques improve the findings or better model default probabilities than ratings.

Scoring applied to firms was developed long ago with the pioneering work of Altman (1968). The technique applies to both default probability and rating modelling. It is still usable and similar techniques apply very well to consumer loans. The score is a function of observable ratios and variables. The rating, or default probability, depends on the score value. The scoring technique uses discriminant analysis to separate defaulting firms from non-defaulting firms. The discriminant function weights a number of observable variables to obtain a score. Depending on the value of the score, the firm is more or less likely to default. Once the score value is known, the default probability, conditional on the score value, differs from one firm to another.

The logit-probit technique allows direct modelling of the relationship between the observable variables and the rating class or the default probability. This is the RiskCalc methodology, as implemented by Moodys to measure default probabilities. Logit-probit techniques apply for modelling zero-one variables (default or no default), categories (such as ratings) or numerical values in the zero to one range, such as default probabilities.

The neural networks approach offers theoretical benefits over multivariate statistical fits. In general, there are correlations between the firms attributes influencing statistically the ratings or the default probability. In addition, the relationship between default probabilities and observable attributes of firms is not linear. Neural networks accommodate interdependencies and non-linear relationships. These features might improve accuracy.

The option theoretic approach to default considers that equity holders have the option to sell the firms assets rather than repay the debt if the asset value gets below the debt value. This is the Merton model of default (Merton, 1974). The option theoretic approach sees equity as a put option on the underlying assets of the firm sold to the lender with a strike equal to the debt amount. KMV Credit Monitor made this technique very popular by providing the expected default frequency (Edf ©) using equity prices to derive asset value and compare it to the firms debt. This is an expected default probability since equity prices look forward, as opposed to historical default statistics. KMV also provides a Private Firm Model that applies to private firms, for which equity values do not exist.

CPV proposes an econometric modelling of default and transition rates (Wilson, 1997a, b). The technique links the default rates of portfolio segments to the cyclical dynamics of industries and countries. The model uses two basic blocks. The first block models default rates of segments as a logit function of economic variables (see Chapter 37 for a description of logit functions). The logit function ensures that the default rates are in the range 0 to 1 whatever the economic factor values. The second block uses a time series predictive model of economic factors that are input into the logit function. This allows looking forward and using predicted rather than past values of the economic index used by the logit function. Plugging these predicted values into the logit function results in predicted default rates. The model requires time series of default rates and economic factors that drive the credit standing of all obligors, since they are representative of country-industry conditions. As a prerequisite, it is necessary to measure default rates for portfolios, not individual default events. This makes it necessary to break down the portfolio into subsets by risk class plus any other relevant criteria. Among other contributions, this approach addresses directly the issue of linking default probabilities to the economic cycles, intuitively seen as major determinants of credit risk.

Another modelling technique for default probabilities consists of inferring them from observed market credit spreads. Credit spreads are the differences between the risk-free government rates and the yields of risky bonds. Credit spreads value credit risk, both default and migration risk plus recoveries, among other factors such as liquidity and risk aversion. The technique extracts the implied default probabilities from observed spreads. This requires modelling credit spreads as a function of credit risk characteristics. Simple models state that the value of a risky debt is equal to the discounted value of the expected cash flows, given the default probability, at the risk-free rate or, alternatively, to the discounted value at the risky market yield (credit spread included) of the contractual cash flows. From this equality, it is possible to find default probabilities, given a recovery rate, such that this equality holds. Because of market risk aversion, the corresponding default probabilities are risk-neutral, meaning that they apply under no risk aversion in the market.