Skip to main content

Term premium: Dynamics with estimation bias correction

Published: Aug 16, 2025
Volume: 23
Keywords: Yield curve Affine term structure model Term premium Small sample bias correction

Authors

Milene Maiser Moraes
Universidade Federal de Santa Catarina
João Frois Caldeira
Universidade Federal de Santa Catarina

Abstract

This paper employs an arbitrage-free affine dynamic term structure model, incorporating a bias correction in the estimation of factor dynamics, to model the Brazilian yield curve and decompose interest rates into expectations of future short-term rates and the term premium, which compensates investors for the risk associated with holding long-term bonds. The study uses data from Brazilian Interbank Deposit Futures Contracts from December 2005 to July 2024, covering maturities ranging from one month to ten years. The results suggest that the model performs well in capturing both the risk-neutral and real-world dynamics of Brazilian interest rates, allowing for an analysis of the behavior of the term premium across the entire maturity spectrum analyzed. Additionally, the bias correction indicates that the volatility of the risk-neutral rate is usually underestimated.

How to cite

Milene Maiser Moraes, João Frois Caldeira. Term premium: Dynamics with estimation bias correction. Brazilian Review of Finance, v. 23, n. 1, 2025. p. e202513. DOI: 10.12660/rbfin.v23n1.2025.93720.


References

ABRAHAMS, M. et al. Decomposing real and nominal yield curves. Journal of Monetary Economics, Elsevier, v. 84, p. 182–200, 2016.
ADRIAN, T.; CRUMP, R. K.; MOENCH, E. Pricing the term structure with linear regressions. Journal of Financial Economics, v. 110, n. 1, p. 110–138, 2013. Disponível em: <https://ideas.repec.org/a/eee/jfinec/v110y2013i1p110-138.html>.
ADRIAN, T.; CRUMP, R. K.; MOENCH, E. Regression-based estimation of dynamic asset pricing models. Journal of Financial Economics, Elsevier, v. 118, n. 2, p. 211–244, 2015.
BAUER, M. D.; RUDEBUSCH, G. D.; WU, J. C. Correcting Estimation Bias in Dynamic Term Structure Models. Journal of Business & Economic Statistics, v. 30, n. 3, p. 454–467, April 2012. Disponível em: <https://ideas.repec.org/a/taf/jnlbes/v30y2012i3p454-467.html>.
BIS. Zero-coupon yield curves: Technical documentation. [S.l.: s.n.], 2005.
BYRNE, J. P.; CAO, S.; KOROBILIS, D. Forecasting the term structure of government bond yields in unstable environments. Journal of Empirical Finance, v. 44, p. 209–225, 2017. ISSN 0927-5398. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0927539817300804>.
CALDEIRA, J. F. Estimação da estrutura a termo da curva de juros no Brasil através de modelos paramétricos e não paramétricos. Análise Econômica, UFRGS, v. 29, p. 95–122, 2011.
CALDEIRA, J. F. Investigating the expectation hypothesis and the risk premium dynamics: new evidence for Brazil. Empirical Economics, v. 59, n. 1, p. 395–412, July 2020. Disponível em: <https://ideas.repec.org/a/spr/empeco/v59y2020i1d10.1007_s00181-019-01629-0.html>.
CHRISTENSEN, J. H. E.; LOPEZ, J. A.; RUDEBUSCH, G. D. Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields. Journal of Money, Credit and Banking, v. 42, n. s1, p. 143–178, September 2010. Disponível em: <https://ideas.repec.org/a/wly/jmoncb/v42y2010is1p143-178.html>.
FILIPOVIC, D. Term-Structure Models: A Graduate Course. [S.l.]: Springer, 2009.
GERHART, C.; LÜTKEBOHMERT, E. Empirical analysis and forecasting of multiple yield curves. Insurance: Mathematics and Economics, v. 95, n. C, p. 59–78, 2020. Disponível em: <https://ideas.repec.org/a/eee/insuma/v95y2020icp59-78.html>.
JOYCE, M. A.; LILDHOLDT, P.; SORENSEN, S. Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves. Journal of Banking & Finance, v. 34, n. 2, p. 281–294, February 2010. Disponível em: <https://ideas.repec.org/a/eee/jbfina/v34y2010i2p281-294.html>.
LITTERMAN, R. B.; SCHEINKMAN, J. A. Common factors affecting bond returns. The Journal of Fixed Income, Elsevier, v. 1, n. 1, p. 54–61, 1991.
NELSON, C. R.; SIEGEL, A. F. Parsimonious modeling of yield curves. Journal of Business, v. 60, n. 4, p. 473–489, 1987.
SMITH, D. J. Bond Math: The Theory Behind the Formulas. [S.l.]: Wiley Finance, 2014.
SVENSSON, L. E. Estimating and interpreting forward interest rates: Sweden 1992–1994. [S.l.], 1994.
VICENTE, J.; KUBUDI, D. Extracting inflation risk premium from nominal and real bonds using survey information. Journal of Economic Studies, v. 45, n. 2, p. 307–325, May 2018. Disponível em: <https://ideas.repec.org/a/eme/jespps/jes-03-2017-0066.html>.