Estimating Exponential Affine Models with Correlated Measurement Errors: Applications to Fixed Income and Commodities

Abstract

Exponential affine models (EAMs) are factor models popular in financial asset pricing requiring a dynamic term structure, such as for interest rates and commodity futures. When implementing EAMs it is usual to first specify the model in state space form (SSF) and then to estimate it using the Kalman filter. To specify the SSF, a structure of the measurement error must be provided which is not specified in the EAM itself. Different specifications of the measurement errors will result in different SSFs, leading to different parameter estimates. In this paper we investigate the influence of the measurement error specification on the parameter estimates. Using market data for both fixed income and commodities we provide evidence that measurement errors are cross-sectionally and serially correlated, which is not consistent with the independent identically distributed (iid) assumptions commonly adopted in the literature. Using simulated data we show that measurement error assumptions affect parameter estimates, especially in the presence of serial correlation. We provide a new specification, the augmented state space form (ASSF), as a solution to these biases and show that the ASSF gives much better estimates than the basic SSF.

Keywords: exponential affine model, state space form, Kalman filter, EM algorithm, measurement errors, serial correlation, commodity futures, yield curves

JEL Classification: G12, G13