Granularity in Qualitative Factor Model
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چکیده
This paper provides a unified setting for factor models applied to panels of qualitative observations. This setting includes as special cases the single risk factor model and its multiple factor extensions used in credit risk analysis, the stochastic migration models used for rating dynamics, and the factor models for prospective mortality tables. We consider the behavior of these models when the cross-sectional dimension is large and derive the granularity adjustments for the maximum likelihood estimators of the factor sensitivities. It is the necessary step before analyzing the effect of estimation risk on measures of credit portfolio risk. The methodology is illustrated by a Monte-Carlo study of the finite sample properties of the estimators.
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