Date
2002
Publisher city
Paris
Publisher
Université Paris-Dauphine
Collection title
Cahier de recherche CEREG (DRM)
Collection Id
2002-11
Dewey
Economie financière
Sujet
Simple Kalman filter; Extended Kalman filter; State-space models; Non observable data; Term structure; Commodity prices; Futures prices
JEL code
G13
Type
Document de travail / Working paper
Item number of pages
24
Abstract (EN)
A Kalman filter can be used for the estimation of a model’s parameters, when the
model relies on non observable data. In finance, this kind of problem arises for example with
term structure models of interest rates, term structure models of commodity prices, and with the
market portfolio in the capital asset pricing model. The Kalman filter is also an interesting
method when a large volume of information must be taken into account, because it is very fast.
Last but not least, when associated with an optimization procedure, the filter provides a mean to
obtain the model’s parameters. In a first section, this article exposes the basic principles of the
method, shows how we can use it to estimate a model’s parameters, and presents two Kalman
filters. The first one is the simple filter, which accepts only linear models. The second one, the
extended filter, allows working with non-linear models. The second section is devoted to the
application of the Kalman filter in finance. To explain how this method can be used in this field,
we apply it to a very famous term structure model of commodity prices, and we discuss
practical problems usually not mentioned in the literature, regarding the implementation of the
method. The third section presents and compares the performances obtained with the two filters.