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 […]
Correlating credit risk events, defaults or migrations, necessitates correlating their risk drivers. Unlike market risk drivers, credit risk drivers are unobservable. They are asset values of firms or economic indexes related to country-industry factors (CPV). In addition, the link between credit risk drivers and credit events is not as simple as the variation of value […]
This section discusses joint migration probabilities within the option theoretic approach of default and migration. The drivers of credit risk are asset values and the level of debt. Credit risk events include default events and credit migration events. We discuss both sequentially.
Credit Metrics develops a technique to find the distribution of values of a portfolio at a future time point from transition matrices. The technique requires using correlated transition probabilities for each pair of obligors. Correlated migration probabilities result from the correlations of unobservable asset values.
Figure 44.5 provides an overview of the modelling of correlations between individual risks, from common risk drivers and factors. Chapter 31 explains the essentials of factor models. The revaluation block models the relationship between credit risk drivers and credit events, but it does not generate any correlation as such.
Table 45.1 provides an overview of the model specifics for generating portfolio value distributions at the horizon. The analytical distributions and the joint migration matrices are not as general as the Monte Carlo simulations. For Monte Carlo simulations, multi-factor models serve to generate correlated asset returns of correlated economic indexes, from which defaults and migrations […]
This section develops the case of a simple portfolio with two obligors A and B subject to correlated default risks. Table 46.1 describes the portfolio, with the unconditional (or standalone) default probabilities and the exposures of each. The loss given default is 100% of exposure.
We proceed with the same portfolio as for the independence case, except that the correlation between default events is now 10%. It is possible to derive all joint event probabilities from the joint default probability as a starting point. The conditional probabilities now differ from the unconditional default probabilities.
When default events are independent, and have the same probability, the distribution of the number of defaults in a portfolio is the binomial distribution. Unfortunately, the binomial distribution cannot capture the effect of size discrepancies and correlations. We use it here to see what happens when the number of obligors increases.
The limit distribution results from conditioning by one random factor the distribution of asset values within a portfolio. With full Monte Carlo simulations, we need to draw a large number of asset values for each firm consistent with the correlation structure of asset values. Chapter 48 illustrates the technique.
