Term-structure dynamics and the determination of state-variables– a multi-factor approach

In this paper we extend the traditional approach in the literature that uses Principal Component Analysis (PCA) when analyzing the dynamic in the yield-curve by taking into account the dynamic part of the process.

Using a Gaussian framework we establish the relationship between the statistical and dynamic aspects of the linear factor structure taking a probability-based framework as our starting point. In this connection we show that the identification of the state variables gives rise to a Markovian stochastic system. This Markovian structure is set up by first assuming that the dynamics in the state variables follow a multi-factor extended Vasicek model and second that the dynamics in the forward rates is defined in an m-factor model in the HJM framework.

Relying on this approach we suggest a dynamic factor model which is estimated on the Danish market for the period 2 January 1990 – 30 June 1998 using the linear Kalmar filter technique.

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