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Volume 5/Number 4, Winter 2009/10 Research Papers Granularity in a qualitative factor model Christian Gourieroux
Department of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario M5S 3G7, Canada; email: gouriero@ensae.fr and Center for Research in Economics and Statistics (CREST), 15 Boulevard Gabriel Peri, 92245 Malakoff, France Alain Monfort
Center for Research in Economics and Statistics (CREST), Laboratoire de Finance-Assurance, 15 Boulevard Gabriel Peri, 92245 Malakoff, France; email: monfort@ensae.fr and Faculty of Economics and Business Administration, Maastricht University, PO Box 616, 6200 MD, Maastricht, The Netherlands 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. The behavior of these models when the cross-sectional dimension is large is considered and granularity adjustments for the maximum-likelihood estimators of the factor sensitivities are derived. These steps are necessary in order to analyze 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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