MODULI SPACE FOR GAUSSIAN TERM STRUCTURE MODELS WITH FINITE DIMENSIONAL REALIZATIONS

Abstract

In this paper, we show that the set of deterministic volatility [10] term structure models with finite dimensional realizations (fdrs) considered in [2] can be identified with an open subset of a Euclidean space, and hence be equipped with the topological and analytical properties of the latter. In particular, the notions of distance, and differentiability of functions defined on this set, can be defined which have important implications for parameter estimation and risk analysis. It is also shown that Lie algebras, which play a key role in the characterization of term structure models with fdrs in [3] and [7], do not separate, and are hence unable to parameterize, these models.