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

38 Pages Posted: 24 Aug 2009

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

Ke Tang

Institute of Economics, School of Social Sciences, Tsinghua University

Date Written: August 21, 2009

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

Suggested Citation

Dempster, M. A. H. and Tang, Ke, Estimating Exponential Affine Models with Correlated Measurement Errors: Applications to Fixed Income and Commodities (August 21, 2009). 22nd Australasian Finance and Banking Conference 2009. Available at SSRN: https://ssrn.com/abstract=1458853 or http://dx.doi.org/10.2139/ssrn.1458853

M. A. H. Dempster

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

Ke Tang (Contact Author)

Institute of Economics, School of Social Sciences, Tsinghua University ( email )

No.1 Tsinghua Garden
Beijing, 100084
China
13466777332 (Phone)

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