Edited by Adrian R. Bell, Chris Brooks and Marcel Prokopczuk
Chapter 4: Estimating term structure models with the Kalman filter
Models for the term structure of interest rates and for the term structure of commodity futures prices are of central interest for academics and practitioners alike. Consequently, an enormous literature on these topics exists. The estimation of term structure models is complicated by the fact that the relevant data have two dimensions. The first is calendar time, that is, the underlying variables evolve over time. The second is time-to-maturity, that is, at each point in time several bonds or futures with different maturity dates are available. Theoretical models link these two dimensions, usually by assuming no-arbitrage. On the empirical front, the Kalman filter allows the researcher to exploit the two dimensions, calendar time and time-to-maturity, simultaneously and thus enables the use of all available data in a consistent way. The aim of this chapter is to explain how term structure models can be efficiently estimated using the Kalman filter. We first describe the general idea of the Kalman filter and then demonstrate its implementation for a joint three-factor model of commodity futures and interest rates. The remainder of this chapter is organized as follows. Section 4.2 introduces the Kalman filter and describes how it can be used for parameter estimation. In section 4.3, we first introduce the three-factor model under study.
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