Microinformation, Nonlinear Filtering and Granularity

59 Pages Posted: 13 Jun 2010 Last revised: 23 Jun 2010

See all articles by Patrick Gagliardini

Patrick Gagliardini

USI Università della Svizzera italiana; Swiss Finance Institute

Christian Gourieroux

University of Toronto - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE); National Bureau of Economic Research (NBER)

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST); National Bureau of Economic Research (NBER); Maastricht University

Date Written: May 1, 2010

Abstract

The recursive prediction and filtering formulas of the Kalman filter are difficult to implement in nonlinear state space models. For Gaussian linear state space models, or for models with qualitative state variables, the recursive formulas of the filter require the updating of a finite number of summary statistics. However, in the general framework a function has to be updated, which makes the approach computationally cumbersome. The aim of this paper is to consider the situation of a large number n of individual measurements, the so-called microinformation, and to take advantage of the large cross-sectional size to get closed-form prediction and filtering formulas at order 1=n. The state variables have a macro-factor interpretation. The results are applied to the maximum likelihood estimation of a macro-parameter, and to the computation of a granularity adjusted Value-at-Risk (VaR) for large portfolios. The methodology of granularity adjustment for VaR is illustrated by an application of the Value of the Firm model [Merton (1974)] to both default and loss given default.

Keywords: Kalman Filter, Nonlinear State Space, Granularity, Repeated Observations, Value-at-Risk, Credit Risk, Loss Given Default, Basel 2

JEL Classification: G12, C23

Suggested Citation

Gagliardini, Patrick and Gourieroux, Christian and Monfort, Alain, Microinformation, Nonlinear Filtering and Granularity (May 1, 2010). Swiss Finance Institute Research Paper No. 10-23. Available at SSRN: https://ssrn.com/abstract=1623657 or http://dx.doi.org/10.2139/ssrn.1623657

Patrick Gagliardini (Contact Author)

USI Università della Svizzera italiana ( email )

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Switzerland

Swiss Finance Institute ( email )

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Christian Gourieroux

University of Toronto - Department of Economics ( email )

150 St. George Street
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Canada
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416-978-6713 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

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Canada

Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE) ( email )

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France
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National Bureau of Economic Research (NBER)

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United States

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )

15 Boulevard Gabriel Peri
Malakoff Cedex, 1 92245
France
+33 1 4117 6079 (Phone)
+33 1 4117 6046 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Maastricht University

P.O. Box 616
Maastricht, 6200MD
Netherlands

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