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Microinformation, Nonlinear Filtering and Granularity

Author

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  • Patrick GAGLIARDINI

    (University of Lugano and Swiss Finance Institute)

  • Christian GOURIEROUX

    (CREST, CEPREMAP (Paris) and University of Toronto)

  • Alain MONFORT

    (CREST, Banque de France and Maastricht University)

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.

Suggested Citation

  • Patrick GAGLIARDINI & Christian GOURIEROUX & Alain MONFORT, 2009. "Microinformation, Nonlinear Filtering and Granularity," Swiss Finance Institute Research Paper Series 10-23, Swiss Finance Institute, revised May 2010.
  • Handle: RePEc:chf:rpseri:rp1023
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    Cited by:

    1. Christophe Boucher & Benjamin Hamidi & Patrick Kouontchou & Bertrand Maillet, 2012. "Une évaluation économique du risque de modèle pour les investisseurs de long terme," Revue économique, Presses de Sciences-Po, vol. 63(3), pages 591-600.
    2. Gagliardini, Patrick & Gouriéroux, Christian, 2013. "Correlated risks vs contagion in stochastic transition models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2241-2269.

    More about this item

    Keywords

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

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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