When modelling to predict a target variable, the relationship between some set of explanatory variables and this target may be unknown or complex. In the context of linear models, transformation by a link function may not be sufficient to capture the linear dependence. In this case it is suitable to model an implicit variable of the target rather than the target directly. For , the dollar value may be difficult to model as a target, and hence many modellers opt for as a proportion of the facility's credit limit or balance. This proportion is what we refer to as herein. However, there are other options available to us as targets. Two of these targets are:
1. Credit Conversion Factor (CCF)
2. Facility Utilization Change (FUC)
To model , consider which can be expressed in dollar amount as (Yang and Tkachenko, 2012):
where is given by
The is the facility outstanding dollar amount at current time, is the facility outstanding dollar amount at default time, is the facility outstanding dollar amount at current time, and is the facility undrawn dollar amount at current time. For estimation of , the Basel II Accord implies the use of modelling rather than directly. This partially stems from attempting to model , which ranges significantly across accounts, even if those accounts happen to share similar risk profiles. Since the resulting expression for is piecewise, it is suggested that accounts with only be modelled, as accounts with pose a known exposure risk to the bank.
Since we are ultimately concerned with predicted as a proportion of authorized limit or balance, we may convert via:
which is equivalent to
and 1 if .
Another target is the , defined as
where as before is the facility outstanding dollar amount at current time, is the facility outstanding dollar amount at default time, and is the facility outstanding dollar amount at current time. Common practice suggests capping at 1 and flooring at 0, and is utilized here (Yang and Tkachenko, 2012).
Since we are concerned with obtaining as a proportion of authorized limit or balance, we may solve for the following expression to recover :
Yang, Bill Huajian, Mykola Tkachenko, "Modeling Exposure at Default and Loss Given Default: Empirical approaches and technical implementation", Journal of Credit Risk, Vol. 8, No. 2, (Summer 2012), pp. 81-102.