 Microinformation, Nonlinear Filtering and GranularityPatrick Gagliardini (), Christian Gourieroux and Alain Monfort No 10-23, Swiss Finance Institute Research Paper Series from Swiss Finance Institute 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 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1023 Access Statistics for this paper More papers in Swiss Finance Institute Research Paper Series from Swiss Finance Institute Contact information at EDIRC. |
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