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Microinformation, Nonlinear Filtering, and Granularity

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  • Patrick Gagliardini
  • Christian Gouriéroux
  • Alain Monfort

Abstract

The recursive prediction and filtering formulas of the Kalman filter are difficult to implement in nonlinear state space models since they require the updating of a function. The aim of this paper is to consider the situation of a large number n of individual measurements, 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 macrofactor interpretation. The results are applied to maximum likelihood estimation of a macroparameter and to computation of a granularity adjusted Value-at-Risk (VaR) for large portfolios. The granularity adjustment for VaR is illustrated by an application of the value of the firm model (Merton, 1974, Journal of Finance 29, 449--470) taking into account both default and loss given default. Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Suggested Citation

  • Patrick Gagliardini & Christian Gouriéroux & Alain Monfort, 2010. "Microinformation, Nonlinear Filtering, and Granularity," Journal of Financial Econometrics, Oxford University Press, vol. 10(1), pages 1-53, 2012 10 1.
    • Handle: RePEc:oup:jfinec:v:10:y:2010:i:1:p:1-53
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbr010
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    Cited by:

    1. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 237-280, Spring.
    2. 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.
    3. 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

    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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