Business — Banking — Management — Marketing & Sales

The correlation building blocks of models capture the obligors credit risk correlation across borrowers and/or with external factors. This is a critical modelling block because: the correlations of credit risks are positive, increasing the risk of losses; they drive the shape of loss distributions and generate fat tails highly sensitive to correlations; they relate to external conditions and economic cycles.

The principle for finding unobservable correlations between credit events (default or migrations) or, equivalently, joint default or migration probabilities is to view these credit events as dependent on correlated risk drivers. These are asset values in the option theoretic approach or explicit external economic factors of Credit Portfolio View (CPV). The correlation between credit events derives from the correlations between these common risk drivers.

Credit risk drivers, such as asset values or economic indexes that drive defaults and migrations, are unobservable directly. This contrasts with market parameters, the market risk drivers, whose observations are continuously available. To turn around the difficulty, models measure correlations between the direct drivers of credit risk through their common dependence on observable risk factors.

Correlation modelling for credit risk follows a two-step process: first, from observable risk factors to unobservable direct credit risk drivers and second, from unobservable direct drivers correlations to credit events, defaults and migrations correlations. For this reason, we make a distinction between credit risk drivers, intermediate variables influencing directly credit risk events, and observable risk factors, or parameters that correlate these risk drivers.

To model correlations, the common principle for all portfolio models is to relate individual risks of each transaction to a set of common factors. The intuition is that such factors as the state of the economy drive the default probabilities. They also affect migration probabilities, since all firms tend to migrate to worse credit states when conditions deteriorate.

KMV uses the option approach to find the joint probability that the correlated values of the assets of two firms hit the threshold value of debts. Credit Metrics uses joint migration matrices providing the joint transition probability of migrating to various credit states for pairs of obligors. The technique models the distribution of pairs of final credit classes for any pair of obligors with given initial credit risk classes. The equity correlations serve as proxies for asset correlations. CPV derives default correlations from their common dependence on economic factors. CreditRisk+ offers the possibility of making default intensities of mixed Poisson distributions of each portfolio segment dependent on common factors. The correlations between risk drivers result from the coefficients of the factor models, and the specific credit risk from the error term that captures the credit risk unrelated to common factors.

The first section details how correlated asset returns drive the correlations between discrete events, such as defaults and migrations. The second section explains how to correlate credit events under the option approach of default. The third section details the Credit Metrics technique, based on joint migration probabilities, for generating correlated migrations for pairs of obligors. The last section addresses multi-factor models of credit risk, with subsections detailing the specifics of credit risk models: KMV Portfolio Manager, Credit Metrics, CPV, CreditRisk+. Chapter 31 summarizes the essentials of multi-factor models.