5.2 Construction of portfolio credit risk models
To construct a credit risk model we have to consider
individual risk elements such as
- (1i)
- Default Probability: the probability that the obligor
or counterparty will default on its contractual obligations to
repay its debt,
- (2i)
- Recovery Rates: the extent to which the face value of
an obligation can be recovered once the obligor has defaulted,
- (3i)
- Credit Migration: the extent to which the credit
quality of the obligor or counterparty improves or deteriorates;
and portfolio risk elements
- (1p)
- Default and Credit Quality Correlation: the degree to
which the default or credit quality of one obligor is related to
the default or credit quality of another,
- (2p)
- Risk Contribution and Credit Concentration: the
extent
to which an individual instrument or the presence of an obligor in
the portfolio contributes to the totality of risk in the overall
portfolio.
From the above building blocks a rating-based credit risk model is generated by
- (1m)
- the definition of the possible states for each obligor's
credit quality, and a description of how likely obligors are to be
in any of these states at the horizon date, i.e. specification of rating classes and
of the corresponding matrix of transition probabilities (relating to (1i) and (3i)).
- (2m)
- quantifying the interaction and correlation between credit
migrations of different obligors (relating to (1p)).
- (3m)
- the re-evaluation of exposures in all possible credit states,
which in case of default corresponds to (2i) above; however, for non-default states
a mark-to-market or mark-to-model (for individual assets) procedure is required.
During this study we will focus on the effects of default dependence
modelling. Furthermore, we assume that on default we are faced with a zero
recovery rate. Thus, only aspects
(1i) and (1p) are of importance in our
context and only two rating classes - default and non-default - are needed.
A general discussion of further aspects can be found in any of the
books Caouette et al. (1998), Ong (1999), Jorion (2000)
and Crouhy et al. (2001).
For practical purposes we emphasize the importance of a
proper mark-to-market methodology (as pointed out in
Kiesel et al. (1999)). However, to study the effects of dependence
modelling more precisely, we feel a simple portfolio risk model is sufficient.
As the basis for comparison we use Value at Risk (VaR)
- the loss which will be exceeded on some
given fractions of occasions (the confidence level) if a portfolio
is held for a particular time (the holding period).