Observational Equivalence of Discrete String Models and Market Models

Abstract

In this paper we show that contrary to the claim made in Longstaff, Santa-Clara, and Schwartz (2000a) and Longstaff, Santa-Clara, and Schwartz (2000b) discrete string models are not more parsimonious than market models. In fact, they are found to be observationally equivalent. We derived that for the estimation of both a K-factor discrete string model and a K-factor Libor market model for N forward rates the number of parameters needed to be estimated equals NK-K(K-1)/2 and not K(K+1)/2 and NK, respectively. We do believe that from an economic point of view the interpretation of the decomposition of the covariance (or correlation) matrix in the discrete string model deserves preference over the market model.

Keywords: String model, market model

JEL Classification: G12