3.6.1
| This section applies to institutions choosing to use transition matrices as a methodology to model PD term structures.
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3.6.2
| Transition matrices are convenient tools; however, institutions should be aware of their theoretical limitations and practical challenges. Their design and estimation should follow the decision process outlined in the MMS. Institutions should assess the suitability of this methodology vs. other possible options as part of the model development process. If a third party consultant suggests using transition matrices as a modelling option, institutions should ensure that sufficient analysis is performed, documented and communicated to the Model Oversight Committee prior to choosing such modelling path.
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3.6.3
| One of the downsides of using transition matrices is the excessive generalization and the lack of industry granularity. To obtain robust matrices, pools of data are often created with obligors from various background (industry, geography and size). This reduces the accuracy of the PD prediction across these dimensions. Consequently, institutions should analyse and document the implications of this dimensionality reduction.
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3.6.4
| The construction of the TTC matrix should meet a set of properties, that should be clearly defined in advance by the institution. The matrix should be based on the institution’s internal data as it is not recommended to use external data for this purpose. If an institution does not have sufficient internal data to construct a transition matrix, or if the matrix does not meet the following properties, then other methodologies should be considered to develop PD term structures.
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3.6.5
| At a minimum, the following properties should be analysed, understood and documented:
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| | (i)
| Matrix robustness: Enough data should be available to ensure a robust estimation of each rating transition point. Large confidence intervals around each transition probabilities should be avoided. Consequently, institutions should estimate and document these confidence intervals as part of the model development phase. These should be reviewed as part of the model validation phase. |
| | (ii)
| Matrix size: The size of the transition matrix should be chosen carefully as for the size of a rating scale. A number of buckets that is too small will reduce the accuracy of decision making. A number of buckets that is too large will lead to an unstable matrix and provide a false sense of accuracy. Generally, it is recommended to reduce the size of the transition matrix compared to the full rating scale of the institution. In this case, a suitable interpolation method should be created as a bridge from the reduced matrix size, back to the full rating scale. |
| | (iii)
| Matrix estimation method: Amongst others, two estimation methods are commonly employed; the cohort approach and the generator approach. The method of choice should be tested, documented and reviewed as part of the model validation process. |
| | (iv)
| Matrix smoothing: Several inconsistencies often occur in transition matrices, for instance (a) transition probabilities can be zero in some rating buckets, and/or (b) the transition distributions for a given origination rating can be bi-modal. Institutions should ensure that the transition matrix respect Markovian properties.
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3.6.6
| If the institution decides to proceed with the transition matrix appraoch, the modelling approach should be clearly articulated as a clear sequence of steps to ensure transparency in the decision process. At a minimum, the following sequence should be present in the modelling documentation. The MMG does not intend to elaborate on the exact methodology of each step. Rather, the MMG intends to draw attention to modelling challenges and set minimum expected practices as follows:
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| | (i)
| TTC transition matrix: The first step is the estimation of a TTC matrix that meets the properties detailed in the previous article. |
| | (ii)
| Credit Index: The second step is the construction a Credit Index (“CI”) reflecting appropriately the difference between the observed PIT DR and TTC DR (after probit or logit transformation). The CI should be coherent with the TTC transition matrix. This means that the volatility of the CI should reflect the volatility of the transition matrix through time. For that purpose the CI and the TTC transition matrix should be based on the same data. If not, justification should be provided. |
| | (iii)
| Forecasted CI: The third step involves forecasting the CI with a macroeconomic model. However, a segmentation issue often arises. If the matrix was created by pooling obligors from several segments, then only one blended CI will be estimated. This may be insufficient to capture the relationship between macroeconomic variables and the creditworthiness of obligors at segment level for the purpose of PIT modelling. Institutions should be cognisant of such limitation and provide solutions to overcome it. An option is to adjust the blended forecasted CI to create several granular CIs that would reflect the behaviour of each segment. |
| | (iv)
| Adjusted transition matrix: The fourth step is the development of a mechanism to adjust the TTC transition matrix with the forecasted CI or the adjusted CIs. Several forward PIT transition matrices should be obtained at several points in the future. |
| | (v)
| PD term structure: Finally, a PD term structure should be created based on the forward PIT transition matrices. Methodologies based on matrix multiplication techniques should be robust and consistently applied.
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3.6.7
| As part of the development process, several pre-implementation validation checks should be performed on the TTC transition matrix in order to verify that the above properties are met. In addition, for each segment being modelled, the matrix should be constructed such that two logical properties are met by the PD outputs:
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| | (i)
| The weighted average TTC PD based on the default column of the TTC transition matrix should be reasonably close to the long term default rate of the obligors from the same segment(s) employed to build the matrix. |
| | (ii)
| The weighted average PIT PD based on the default column of the PIT transition matrix for the next few time steps, should be coherent with the current default rate of the obligors from the same segment(s) employed to build the matrix or the segment(s) employed to derived the adjusted CIs.
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