# Credit Portfolio Models

The purpose of this chapter is to provide an overview of the main "vendors" models, building on the principles of credit portfolio modeling already explained. We review here four models:

• Moody's-KMV Portfolio Manager

• Credit Metrics

• Credit Portfolio View ("CPV")

• CreditRisk+.

The two first models are self-contained, and can be relatively readily implemented by end-users. They are full valuation models and rely on Monte Carlo simulations for generating a distribution of portfolio values at a final horizon, from which loss statistics are derived. The other models provide an open framework. Credit Portfolio View is an econometric model of default rates using observable economic and country-industry factors. CreditRisk+ relies on actuarial techniques and provides an analytical distribution of default, within an open framework. A comparative view of models is in Gordy [32].

The four models provide a global view of the lines along which credit portfolio models can be constructed. The only omitted "best practice" model is the dependent times to default model, which is extensively used because it is easy to implement, and which is described in the previous chapter (Chapter 50).

The presentation of credit portfolio models follows a structure by building block as described in the first section, which provides a summarized overview of all four models. The overview lists the main building blocks of each model: The underlying conceptual framework is introduced first, how defaults and migration events are modeled, the dependencies building block applying to risk factors, the revaluation at horizon, and the simulation block. Subsequent sections describe the specifics of each model.

## CREDIT PORTFOLIO MODEL OVERVIEW

The structure of the presentation deals with the main building blocks that tend to be common to all credit portfolio models (Table 51.1). The sources are in [80], [81] and [82].

1 The underlying conceptual framework, such as the structural model of default (Moody's-KMV) or the econometric approach (CPV).

2 The modeled credit events, ranging from default events only to full migrations, with special cases where the target variables are default and migration rates of sub-portfolios.

3 Modeling dependencies and risk factors.

4 Revaluation at the final horizon implemented by models, when applicable (full migration mode).

5 Generating portfolio values and portfolio loss distributions at horizon, such as Monte Carlo simulation or the actuarial techniques used in CreditRisk+.