4.5 TTC LGD Modelling

4.5.1	The objective of TTC LGD models is to estimate LGD, independently of the macroeconomic circumstances at the time of default. Therefore, these models should not depend on macroeconomic variables. These models can take several forms depending on the data available and the type of portfolio. Institutions are free to choose the most suitable approach, provided that it meets the minimum expectations articulated in this section.
4.5.2	Defaulted vs. non-defaulted cases: LGD should be modelled and estimated separately between defaulted obligors (or facilities) and non-defaulted obligors. Whilst the methodology should be similar between these two cases, several differences exist:
	(i)	Upon a default event, the estimation of recovery relies on assumptions and on a live process with regular information updates. Therefore, for defaulted obligors (or facilities), as the recovery process unfolds, institutions should collect additional information to estimate recovery rates with further accuracy and thus obtain more specific LGD estimation.
	(ii)	For defaulted obligors (or facilities), particular attention should be given to PV modelling as per the dedicated section of the MMG. Discount factors should reflect the circumstances of default and the uncertainty surrounding the recovery process.
	(iii)	One of the major differences between LGD from defaulted vs. non-default exposures is that the former is estimated only as of the date of default, while the latter is estimated at several point in time, depending on the needs of risk management and financial reporting.
4.5.3	Properties: At a minimum, LGD models should meet the following properties.
	(i)	The modelled LGD should be based upon the historical realised LGD observations previously estimated.
	(ii)	The methodology should avoid excessive and unreasonable generalisations to compensate for a lack of data.
	(iii)	The model performance should be validated based on clear performance measurement criteria. For instance, model predictions should be compared against individual observations and also against segment average.
	(iv)	There should be enough evidence to demonstrate that in-sample fit and out-of-sample performance are reasonable.
	(v)	The choice of parameters should be justified and documented.
	(vi)	The model inputs should be granular and specify enough to generate a LGD distribution that is a fair and accurate reflection of the observed LGDs.
4.5.4	Functional form: Institutions are free to use LGD models with any functional form provided that the model output is an accurate reflection of the observed LGD. Institutions should aim to build LGD models that incorporate the suitable drivers enabling the model to reflect the main possible outcomes of the workout process.
4.5.5	Parameters: Institutions should aim to incorporate the following drivers in their LGD models. This means that any model using less granular inputs should be considered as a first generation model that requires improvement as further data becomes available.
	(i)	The probability of cure without restructuring,
	(ii)	The probability of cure through restructuring,
	(iii)	The collateral coverage,
	(iv)	Direct and indirect recovery costs,
	(v)	Collateral liquidation values including haircuts, and
	(vi)	Recovered cash flows
	The quantitative drivers above should be analysed (segmented) by qualitative drivers, including but not limited to:
	(vii)	Industry or obligor type,
	(viii)	Facility type, and
	(ix)	Seniority ranking.
4.5.6	The parameters listed above should drive the estimation of LGD. The mathematical construction of the LGD model can take several forms, that institutions are free to choose. The form presented below serves as illustration. Institutions are not expected to use this expression literally; rather, they should ensure that their final LGD model respects the principles of this expression with a suitable estimation of each component. If institutions employ a different functional form, they are encouraged to use the following expression as a challenger model.
	Table 7: Typical components of LGD models

Component	Definition
P₁	Probability of cure without restructuring
P₂	Probability of cure through restructuring
S	Collateral coverage defined as 𝐶𝑜𝑙𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 ⁄𝐸𝐴D
L₁	Loss (cost) from managing delinquent clients that were cured without restructuring
L₂	Loss from managing delinquent clients through restructuring or rescheduling, including direct and indirect costs plus NPV impacts.
L₃	Loss from the realisation of collateral including haircuts, direct and indirect costs plus NPV impact. Estimated across all collateral types.
L₄	Loss arising from the incomplete recovery of the portion of exposure not covered by collateral, also including indirect management costs and NPV impacts. (Referred to as unsecured LGD.)

	The loss arising from the unsecured portion (L₄) is often called "unsecured LGD". The final LGD after taking collateral into accounts is often referred to as the "secured LGD". Irrespective of the semantic employed, LGD models should reconcile conceptually against the expression above.
4.5.7	Granularity: Institutions should aim to develop TTC LGD models to estimate LGD at a low level of granularity. The following minimum expected practices apply:
	(i)	Institutions should aim to model LGD at facility level, i.e. the LGD should incorporate facility characteristics. If this is not possible for practical reasons, LGD should be computed at obligor level. This means that LGD should be driven by parameters specific to each obligor and the associated collaterals if any.
	(ii)	If several facilities are secured by one or several collaterals, institutions should implement a clear collateral allocation mechanism from the obligor to each facility.
	(iii)	If institutions do not have the required data to build such granular models, they should put in place a formal project in order to collect the necessary data as a stepping stone towards accurate LGD modelling.
4.5.8	Segmentation: The portfolio segmentation employed to estimate LGDs should be justified and documented. In theory, LGD segments do not have to be identical to those employed for PD modelling. However, in practice, it is recommended to use similar portfolio segmentation across PD and LGD models, where possible, in order to ease the interpretation of LGD and subsequent usage in provision and capital estimation.
4.5.9	Collateral haircuts: The last valuation of an asset is unlikely to reflect the resale value of a repossessed asset. Consequently, institutions should estimate appropriate haircuts based on the assumption that they intend to sell the repossessed asset as soon as reasonably possible. Haircuts should be estimated based on historical data by type of collateral.
4.5.10	Bimodal distribution: Institutions should identify whether the distribution of observed LGD is bimodal, i.e. a distribution with two peaks of high frequency. In this case, specific modelling constraints apply. Institutions should be cautious when using an average value between these two peaks. Such average can be misleading and should not be employed to assign LGD at facility level since it does not correspond to an observable LGD at facility level.
4.5.11	Logical features: Following on from the conceptual framework presented above, some logical characteristics should be respected: (i) the final LGD should be equal or smaller than the unsecured LGD, (ii) the LGD should decrease with the presence of collateral, all other parameters being kept constant, and (iii) the longer the recovery period, the higher the recovery, the lower the LGD. The logical features should be tested as part of the model validation process.