Implicit Targets of EAD

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 EAD, the dollar value may be difficult to model as a target, and hence many modellers opt for EAD as a proportion of the facility's credit limit or balance. This proportion is what we refer to as EAD 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 CCF, consider EAD which can be expressed in dollar amount as (Yang and Tkachenko, 2012):

EAD_\$=bal_0+CCF*undrawn_0

where CCF is given by

CCF= \max(bal_1-bal_0,0)/(undrawn_0 ) if undrawn_0>0

and

CCF=0 if undrawn_0 \leq 0

The bal_0 is the facility outstanding dollar amount at current time, bal_1 is the facility outstanding dollar amount at default time, auth_0 is the facility outstanding dollar amount at current time, and undrawn_0=(auth_0-bal_0 ) is the facility undrawn dollar amount at current time. For estimation of EAD, the Basel II Accord implies the use of modelling CCF rather than EAD directly. This partially stems from attempting to model  EAD_\$ , which ranges significantly across accounts, even if those accounts happen to share similar risk profiles. Since the resulting expression for CCF is piecewise, it is suggested that accounts with undrawn_0>0 only be modelled, as accounts with undrawn_0 \leq 0 pose a known exposure risk to the bank.

Since we are ultimately concerned with predicted EAD as a proportion of authorized limit or balance, we may convert CCF via:

EAD=(bal_0+CCF*undrawn_0)/ \max(auth_0,bal_0 )

which is equivalent to

(bal_0+\max(bal_1-bal_0,0))/auth_0 if undrawn_0>0

and 1 if undrawn_0 \leq 0.

Another target is the FUC, defined as

FUC=(bal_1-bal_0)/(auth_0 )

where as before bal_0 is the facility outstanding dollar amount at current time, bal_1 is the facility outstanding dollar amount at default time, and auth_0 is the facility outstanding dollar amount at current time. Common practice suggests capping FUC at 1 and flooring at 0, and is utilized here (Yang and Tkachenko, 2012).

Since we are concerned with obtaining EAD as a proportion of authorized limit or balance, we may solve for the following expression to recover EAD:

EAD_pred=(bal_0+\max(FUC*auth_0,0))/ \max(auth_0,bal_0).

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.