The Kalman filter in finance: An application to term structure models of commodity prices and a comparison between the simple and the extended filters

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.