With these last specifications in place, the derivation of the correlation structure of the proposed incremental risk model is complete. The result is that the asset correlations between all issuers underlying the positions can be specified in detail (i.e. each correlation coefficient can take on a unique pre-specified value). Consequently, directly estimated historical correlations can be inserted into the model as well as correlations estimated with commonly applied factor models. This feature of the constructed correlation structure makes it much more versatile than the often used bivariate Gaussian specification of systematic and idiosyncratic risk. Moreover, have shown that these single-factor correlation structures, as applied by for example, often perform worst than the simple use of historical correlations. The correlation structure will be used in the model estimations in and its issuer correlation and autocorrelation inputs are estimated in . One final remark is that the complete correlation structure, as presented in this section, is completely interchangeable. The simulation model does not exclusively dependent of this specific structure. Any correlation structure can be combined with the constructed credit rating simulation model as long as the required asset return thresholds (Z-values) can be computed, with the use the assumed distribution of the underlying issuer asset returns in this structure. PART II The incremental risk model that has been INPUT ESTIMATION constructed in is built upon various inputs. In fact, nearly every incremental risk model will be built on similar inputs. Consequently, it would be prudent to discuss various alternative methodologies that can be applied in the estimation of these input parameters as well. Such a set-up generates the opportunity of an assessment of the effects of alternative input estimation methodologies on the output of the proposed model. Herein, the emphasis is entirely placed on the two most imperative inputs of the model: the stand-alone risk specification (the credit migration matrix) and the specification of the relations between the migration and default risk underlying the various individual positions in the portfolio (the issuer correlations and autocorrelations). First, in , three alternative techniques concerning the estimation of the credit migration matrix are addressed, and the underlying conditionality of this matrix is treated as well. Secondly, in , the estimation of issuer asset return correlations is discussed. In this, the two main approaches on this subject, the equity correlation proxy and issuer asset correlation based on default rates, are evaluated.
With these last specifications in place, the derivation of the correlation structure of the proposed incremental risk model is complete. The result is that the asset correlations between all issuers underlying the positions can be specified in detail (i.e. each correlation coefficient can take on a unique pre-specified value). Consequently, directly estimated historical correlations can be inserted into the model as well as correlations estimated with commonly applied factor models. This feature of the constructed correlation structure makes it much more versatile than the often used bivariate Gaussian specification of systematic and idiosyncratic risk. Moreover, have shown that these single-factor correlation structures, as applied by for example, often perform worst than the simple use of historical correlations. The correlation structure will be used in the model estimations in and its issuer correlation and autocorrelation inputs are estimated in . One final remark is that the complete correlation structure, as presented in this section, is completely interchangeable. The simulation model does not exclusively dependent of this specific structure. Any correlation structure can be combined with the constructed credit rating simulation model as long as the required asset return thresholds (Z-values) can be computed, with the use the assumed distribution of the underlying issuer asset returns in this structure. PART II INPUT ESTIMATION The incremental risk model that has been constructed in is built upon various inputs. In fact, nearly every incremental risk model will be built on similar inputs. Consequently, it would be prudent to discuss various alternative methodologies that can be applied in the estimation of these input parameters as well. Such a set-up generates the opportunity of an assessment of the effects of alternative input estimation methodologies on the output of the proposed model. Herein, the emphasis is entirely placed on the two most imperative inputs of the model: the stand-alone risk specification (the credit migration matrix) and the specification of the relations between the migration and default risk underlying the various individual positions in the portfolio (the issuer correlations and autocorrelations). First, in , three alternative techniques concerning the estimation of the credit migration matrix are addressed, and the underlying conditionality of this matrix is treated as well. Secondly, in , the estimation of issuer asset return correlations is discussed. In this, the two main approaches on this subject, the equity correlation proxy and issuer asset correlation based on default rates, are evaluated.
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