Microinformation, Nonlinear Filtering and Granularity
AbstractThe 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.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 10-23.
Length: 59 pages
Date of creation: Nov 2009
Date of revision: May 2010
Kalman Filter; Nonlinear State Space; Granularity; Repeated Observations; Value-at-Risk; Credit Risk; Loss Given Default; Basel 2;
Other versions of this item:
- Patrick Gagliardini & Christian Gouriéroux & Alain Monfort, 2010. "Microinformation, Nonlinear Filtering, and Granularity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(1), pages 1-53, 2012 10 1.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
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