Term Structure Estimation: A Review

Authors

  • Emma Berenguer Universidad Pablo Olvide
  • Ricardo Gimeno Banco de España
  • Juan M. Nave Universidad de Castilla la Mancha

Keywords:

Term Structure of Interest Rates, Estimation Methodologies.

Abstract

There are two distinct approaches to modelling the term structure of interestrates. The first is essenciallly to measure the term structure using statistical techniques by appliyng interpolation or curve-fitting methods to construct yields.The second approach is based on models, known as dynamic models, which make explicit assumptions about the evolution of state variables and asset pricing models using either equilibrium or arbitrage arguments. There is no consensus on any particular methodology and the choice between alternative curve modelsis, in part, subjective. Nevertheless, the interpolation or curve-fitting methods have showed good properties and are those used nowadays by the vast majority of central banks.The objective of this article is to present the principal methodologies that have been proposed for the TSIR estimation. A better understanding of the different methodologies and their limitations will provide the researchers with an overview ofthe problematic of estimation of the yield curve and will enable them to choose the best model according to their objectives.

References

ABAD, P. and NOVALES, A. (2002), Risk premia in the term structure of swaps in pesetas, Serie ICAE Documentos de trabajo de la Universidad Complutense de Madrid.

ABAD, P. and ROBLES, M.D. (2003), “Estructura temporal de los tipos de interés: teoría y evidencia empírica”, Revista Asturiana de Economía, 27.

ADAMS, K. and VAN DEVENTER, R. (1994), “Fitting yields curves and forward rate curves with maximum smoothness”, The Journal of Fixed Income, Junio, pp. 52-62.

ANDERSON, N., BREEDON, F., DEACON, M., DERRY, A. and MURPHY, G. (1996), Estimating and interpreting the yield curve, New York: Wiley.

ANDERSON, N. and SLEATH, J. (2001), New estimates of the U.K real and nominal yield curves, Bank of England Working Paper Series.

BANK FOR INTERNATIONAL SETTLEMENTS (BIS) (2005), Zero-coupon yield curves: technical documentation. BIS papers 25.

BERENGUER, E. (2009), La Estimación de la Estructura Temporal de los tipos de interés: Metodología y Aplicaciones. Unpublished PhD dissertation. Universidad Nacional de Educación a Distancia.

BLISS, R. (1996), “Testing term structure estimation methods”, Working Paper No. 96-12, Federal Reserve Bank of Atlanta.

CARLENTON, W. and COOPER, I. (1976). “Estimation and uses of the Term Structure of Interest rates”, The Journal of Finance, 31.

CARLENTON, W., CHAMBERS, D. and WALDMAN, D. (1984), “A new approach to Estimation of the Term Structure of Interest rates”, Journal of Finance and Quantitative Analysis, 1 ,pp. 233-252.

COHEN, K., KRAMER, R.L. and WAUGH, W.H. (1966), “Regression yield curves for U.S government securities”, Management Science, 13. December.

COX, J., INGERSOLL, J. and ROSS, S. (1985), “A theory of the term structure of interest rates.” Econometrica, 53,March, pp. 385-407.

_ (1981), “A re-examination of traditional hyphothesis about the term structure of interest rates”. Journal of Finance, 36, pp. 769-799.

CULBERTSON, J. (1957), “The term structure of interest rate”, Quaterly Journal of Economics, 71, pp. 485-517.

DAI, Q. and SINGLETON, K. (2000), “ Specification analysis of affine term structure models”, Journal of Finance, 55,pp. 1943-1978.

DE ANDRÉS, J. (2000) Estimación de la estructura temporal de los tipos de interés mediante números borrosos, Unpublished PhD Dissertation. Universidad Rovira i Virgili.

DE ANDRÉS, J. and TERCEÑO, A. (2003). “Estimating a term structure of interest rates for fuzzy financial pricing by using fuzzy regression methods”, Fuzzy Sets and Systems, 139(2), pp. 313-331.

DE BOOR, C. (1978), A practical guide to splines. New York: Springer-Verlag.

DEACON, M. and DERRY, A. (1994), “Estimating the Term Structure of interest Rates”, Bank of England Working Paper Serie, nº.24.

DIAMENT, P. (1993), “Semi-empirical smooth fit to the Treasury Yield Curve”, Journal of Fixed Income, Junio, pp. 55-70.

DIEBOLD, F.X and LI, C. (2006), “Forecasting the term structure of government bond yields”, Journal of econometrics, nº130, pp. 337-364.

DOMINGUEZ, E. and NOVALES, A. (2000), “Testing the Expectations Hyphotesis in Eurodeposits”, Journal of International Money and Finance, 19, pp.713-736.

DUFFIE, D., JUN, P. and SINGLETON, K. (2000), “Transform analysis and asset pricing for affine jump-diffusions”, Econometrica, 68, pp.1343-1376.

DUFFIE, D. and KAN, R. (1996), “A yield-factor model of interest rates”, Mathematical Finance, 25, pp. 379- 406.

DURAND, D. (1942), “Basic yield of Corporate Bonds, 1900-1942”, Technical Paper, Vol.3 NBER.

FAMA, E. (1984), “The information in the term structure”, The Journal of Financial Economics, pp. 509-528.

FISHER, I. (1896), “Appreciation and interest”, Publications of the American Economic Association, pp. 23-29.

FISHER, M., NYCHKA, D. and ZERVOS, D. (1995), “Fitting the term structure of interest rates with smoothing splines”, Finance and Economics Discussion Series 95-1, Federal Reserve Board. Washington D.C.

FREIXAS, X. (1992), Estructura temporal de tipos de interés: hipótesis teóricas y resultados empíricos, Investigaciones Económicas, 16, pp. 187-203.

GIMENO, R. and MARQUÉS, J.M. (2012), “A market based approach to inflation expectations, risk premia and real interest rates”, Spanish Review of Financial Economics, vol. 10, pp. 18-29.

GIMENO, R. and NAVE, J. (2009), “Genetic algorithm estimation of interest rate term structure”, Computational Statistics and Data Analysis, 53, pp. 2236-2250.

GUTHMANN, H. (1929), The relation of the maturity factor to yield differences among investment securities.Unpublished PhD Dissertation: University of Chicago.

HALEY, C. and SCHALL, L. (1979), The Theory of Financial Decisions.MacGraw Hill.

HAUGEN, R.A. (1997), Modern Investment Theory. Prentice-Hall, Inc.

HEATH, D., JARROW and MORTON, A. (1992), “Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation”, Econometrica, 60, pp. 77-105.

HICKS, J. (1939), Value and Capital. London.: Oxford University Press.

HO, T.S. and LEE, S. (1986), “Term structure movements and pricing interest rate contingent claims”, Journal of Finance , 41, pp. 1011-1029.

HULL, J. and WHITE, A. (1990), “Pricing interest-rate derivatives securities”, Review of Financial Studies, 3, pp. 573-592.

IOANNIDES, M. (2003), “A comparison of yield curve estimation techniques using UK data”, Journal of Banking and Finance, 27, pp. 1-26.

LEBER, M., FERNÁNDEZ-NAVAS, J. and SOLER, J. (2001), “Valoración de bonos en el mercado de deuda del Estado con modelos estáticos y dinámicos de la ETTI”, Revista Española de Financiación y Contabilidad XXX..

LIN, B. (2002), “Fitting term structure of interest rates using B-splines: the case of Taiwanese government bond”, Applied Financial Economics, 12, pp. 57-75.

LUTZ, F. (1940), “The structure of interest rates”, Quaterly Journal of Economics, pp. 36-63.

MALKIEL, B. (1962), “Expectations, bond prices and the term structure of interest rates”, Quaterly Journal of Economics, 76, pp. 197-218.

MANKIW, N. and SUMMERS, L. (1984), “Do long-term interest rates overreact to short term interest rates”, Brooking Paper in Economic Activity, pp. 223-247.

MANSI, S. and PHILLIPS, J. (2001), “Modeling the term structure from Onthe-Run Treasury yield curve”, Journal of Financial Research, 24, pp.545-564.

MASSOT, M. and NAVE, J.M. (2003), “La hipótesis de las expectativas a largo plazo: evidencia en el mercado español de deuda pública”, Investigaciones Económicas, 27, pp. 533-564.

MASTRONIKOLA, K. (1991), “Yield curves for gilt-edged stocks: a new model. Bank of England”, Discussion Papers , 49.

MCCULLOCH, J. (1975), “ The tax-adjusted yield curve”, The Journal of Finance, 30, pp. 811-830.

_ (1971), “Measuring the term structure of interest rates”, The Journal of Business, pp. 19-31.

MICHAELSEN, J. (1963),” The term structure of interest rates”, Quaterly Journal of Economics. 78, pp 166-174.

MODIGLIANI, F. and SUTCH, R. (1966), “Innovations in interest rate policy”, American Economic Review, 56, pp.178-197.

MORENO, M. (2000), “Modelización de la estructura temporal de los tipos de interés: valoración de activos derivados y comportamiento empírico”, Revista Española de Financiación y Contabilidad , 29, pp. 345-376.

MORINI, S. (1998), Estimación de la estructura temporal de los tipos de interés: propuestas alternativas.Unpublished PhD dissertation: Universidad de La Laguna.

NAVARRO, E. and NAVE, J. (1997), “A two-factor duration model for interest rate risk management” Investigaciones económicas, Vol. XXI, pp. 55-74.

NELSON, C. and SIEGEL, A. (1987), “Parsimonious modeling of yield Curves”, Journal of Busines,s 60, pp. 473-489.

NUÑEZ, S. (1995), Estimación de la estructura temporal de tipos de interés en España: elección entre métodos alternativos. Documento de trabajo Banco de España 9522, Banco de España.

PIAZZESI (2010), “Affine term structure models”, en AÏT-SAHALIA, Y AND HANSEN, L (ed) Handbook of Financial Econometrics. Amsterdam: North Holland, pp. 691-766.

POWELL, M. (1981), Approximation Theory and Methods. Cambridge: Cambridge University Press.

RAMPONI, A. (2003), “Adaptative and monotone spline estimation of crosssectional term structure”, International Journal of Theoretical and Applied Finance, 6, pp. 195-212.

SCHAEFER, S. (1981), “Measuring a tax-specific term structure of interest rates in the market for British government securities”, The Economic Journal, 91, pp. 415-438.

_ (1979). Consistent bond prices.Unpublished PhD Thesis. University of London.

SHEA, G. (1984), “Pitfalls in smoothing interest rate term structure data: equilibrium models and spline approximations”, Journal of Finance and Quantitative Analysis, 19, pp. 253-269.

SHILLER, R.J. (1990), “The term structure of interest rates”, en FRIEDMAN, B AND HAN, F.H (ED) Handbook of Monetary Economics. Amsterdam: North Holland, pp. 626-723.

STEELEY, J. (1991), “Estimating the gilt-edged term structure: basis splines and confidence intervals”, Journal of Business Finance and Accounting, 18, pp. 513-529.

SVENSSON, L. (1994), “Estimating and interpeting forward interest rates: Sweden 1992-1994”. Working Paper No 114. International Monetary Fund

VASICEK, O. (1977), “An equilibrium characterization of the term structure”, Journal of Financial Economics, 5, pp. 177-188.

VASICEK, O. and FONG, H. (1982), “Term structure modeling using exponential splines”, The Journal of Finance , 37.

WAGGONER, D. (1997), “Spline methods for extracting Interest rate curves from coupon bond prices”, Working Paper No 97-10. Federal Reserve Bank of Atlanta.

Published

2013-09-11

How to Cite

Berenguer, E., Gimeno, R., & Nave, J. M. (2013). Term Structure Estimation: A Review. Icade. Journal of the Faculty of Law at Universidad Pontificia Comillas, (89), 125–154. Retrieved from https://revistas.comillas.edu/index.php/revistaicade/article/view/1125