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Estimating exponential affine models with correlated measurement errors: Applications to fixed income and commodities

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  • Dempster, M.A.H.
  • Tang, Ke

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.

Suggested Citation

  • Dempster, M.A.H. & Tang, Ke, 2011. "Estimating exponential affine models with correlated measurement errors: Applications to fixed income and commodities," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 639-652, March.
    • Handle: RePEc:eee:jbfina:v:35:y:2011:i:3:p:639-652
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    2. Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
    3. Januj Juneja, 2018. "Empirical performance of Gaussian affine dynamic term structure models in the presence of autocorrelation misspecification bias," Review of Quantitative Finance and Accounting, Springer, vol. 50(3), pages 695-715, April.
    4. esposito, francesco paolo & cummins, mark, 2015. "Filtering and likelihood estimation of latent factor jump-diffusions with an application to stochastic volatility models," MPRA Paper 64987, University Library of Munich, Germany.
    5. Juneja, Januj, 2017. "Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 292-305.
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    7. Januj Juneja, 2015. "An evaluation of alternative methods used in the estimation of Gaussian term structure models," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 1-24, January.
    8. Rauch, Johannes & Krayzler, Mikhail & Brunner, Bernhard & Zagst, Rudi, 2013. "Pricing of derivatives on commodity indices," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 143-151.
    9. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 119-129.
    10. Marcel Prokopczuk & Yingying Wu, 2013. "Estimating term structure models with the Kalman filter," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 4, pages 97-113, Edward Elgar Publishing.

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