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https://doi.org/10.1142/S0219024903002262Cited by:7 (Source: Crossref)

Principal Component Analysis (PCA) has been traditionally used for identifying the most important factors driving term structures of interest rates movements. Once one maps the term structure dynamics, it can be used in many applications. For instance, portfolio allocation, Asset/Liability models, and risk management, are some of its possible uses. This approach presents very simple implementation algorithm, whenever a time series of the term structure is disposable. Nevertheless, in markets where there is no database for discount bond yields available, this approach cannot be applied. In this article, we exploit properties of an orthogonal decomposition of the term structure to sequentially estimate along time, term structures of interest rates in emerging markets. The methodology, named Legendre Dynamic Model (LDM), consists in building the dynamics of the term structure by using Legendre Polynomials to drive its movements. We propose applying LDM to obtain time series for term structures of interest rates and to study their behavior through the behavior of the Legendre Coefficients levels and first differences properly normalized (Legendre factors). Under the hypothesis of stationarity and serial independence of the Legendre factors, we show that there is asymptotic equivalence between LDM and PCA, concluding that LDM captures PCA as a particular case. As a numerical example, we apply our technique to Brazilian Brady and Global Bond Markets, briefly study the time series characteristics of their term structures, and identify the intensity of the most important basic movements of these term structures.

References

  • C. I. R. Almeida, Estimation, tests and applications in emerging markets: The term structure of interest rates, Unpublished Ph.D. Thesis, Electrical Engineering Department, PUC-RJ, 2001 . Google Scholar
  • C. I. R. Almeida, A. M. Duarte Jr. and C. A. C. Fernandes, Journal of Fixed Income 1, 21 (1998). Google Scholar
  • C. I. R. Almeida, A. M. Duarte Jr. and C. A. C. Fernandes, Journal of Fixed Income 2, 100 (2000). CrossrefGoogle Scholar
  • C. I. R. Almeida, A. M. Duarte Jr. and C. A. C. Fernandes, Interest rate risk measurement in Latin American emerging markets using orthogonal polynomials, Working Paper, Electrical Engineering Department, PUC-RJ, 2001 . Google Scholar
  • F. Alonso, R. Blanco, A. del Río and A. Sanchís, Estimating liquidity premia in the Spanish government securities market, Bank of Spain. BIS Paper, 2000 . Google Scholar
  • N. Anderson and J. Sleath, Bank of England Quarterly Bulletin  (1999). Google Scholar
  • D.   Backus , S.   Foresi and C.   Telmer , Advanced Fixed Income Valuation Tools ( Wiley and Sons , 1999 ) . Google Scholar
  • J. R. Barber and M. L. Copper, Journal of Portfolio Management 99 (1996), DOI: 10.3905/jpm.1996.409574. Google Scholar
  • R.   Bliss , Advances in Futures and Options Research   9 , 197 . Google Scholar
  • G. E. P.   Box , G. M.   Jenkins and G. C.   Reinse , Time Series Analysis, Forecasting and Control ( Prentice Hall , New Jersey , 1994 ) . Google Scholar
  • W. A.   Brock , D. A.   Hsieh and B.   LeBaron , Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence ( MIT Press , Massachusetts , 1991 ) . Google Scholar
  • J. Y.   Campbell , A. W.   Lo and A. C.   MacKinlay , The Econometrics of Financial Markets ( Princeton University Press , Princeton , 1997 ) . CrossrefGoogle Scholar
  • R. R. Chen and L. Scott, Journal of Fixed Income 3, 14 (1993). CrossrefGoogle Scholar
  • A.   Clare and I.   Lekkos , Decomposing the relationship between international bond markets , BIS Conference Paper , Bank of International Settlements . Google Scholar
  • J. C. Cox, J. E. Ingersoll and S. A. Ross, Econometrica 53, 385 (1985), DOI: 10.2307/1911242. Crossref, Web of ScienceGoogle Scholar
  • M.   Dahlquist , P.   Hordahl and P.   Sellin , Measuring international volatility spillovers , BIS Conference Paper , Bank of International Settlements . Google Scholar
  • R.   Davidson and J. G.   MacKinnon , Estimation and Inference in Econometrics ( Oxford University Press , New York , 1993 ) . Google Scholar
  • F. X. Diebold and C. Li, Forecasting the term structure of government bond yields. Working Paper, University of Pennsylvania, 2002 . Google Scholar
  • J. C. Duan and J. G. Simonato, Estimating and testing exponential-affine term structure models by Kalman Filter, Working Paper, Hong Kong University of Science and Technology, 1997 . Google Scholar
  • G. Duffee and R. Stanton, Estimation of dynamic term structure models. Working Paper, Haas School of Business, U. C. Berkeley, 2001 . Google Scholar
  • D.   Duffie , Dynamic Asset Pricing Theory ( Princeton University Press , Princeton , 1996 ) . Google Scholar
  • D. Duffie and R. Kan, Mathematical Finance 6(4), 379 (1996), DOI: 10.1111/j.1467-9965.1996.tb00123.x. CrossrefGoogle Scholar
  • N. El Karoui, H. Geman and V. Lacoste, Applied Stochastic Models in Business and Industry 16, 197 (2000). Crossref, Web of ScienceGoogle Scholar
  • F. J. Fabozzi and A. Franco, Handbook of Emerging Fixed Income & Currency Markets (FJF Associates, Pennsylvania, 1997) pp. 32–43. Google Scholar
  • D. Filipovic, Mathematical Finance 9(4), 349 (1999), DOI: 10.1111/1467-9965.00073. Crossref, Web of ScienceGoogle Scholar
  • B.   Flury , Common Principal Components and Related Multivariate Models ( John Wiley and Sons , New York , 1988 ) . Google Scholar
  • R. Gallant and G. Tauchen, Econometric Theory 12, 657 (1996), DOI: 10.1017/S0266466600006976. Crossref, Web of ScienceGoogle Scholar
  • G. H.   Golub and C. F.   Van Loan , Matrix Computations ( Johns Hopkins University Press , Maryland , 1985 ) . Google Scholar
  • J. D.   Hamilton , Time Series Analysis ( Princeton University Press , 1994 ) . CrossrefGoogle Scholar
  • J.   James and N.   Webber , Interest Rate Modeling ( John Wiley and Sons , London , 2000 ) . Google Scholar
  • N. N. Lebedev, Special Functions and Their Applications (Dover Publications, New York, 1972) pp. 44–60. Google Scholar
  • R. Litterman and J. A. Scheinkman, Journal of Fixed Income 1, 54 (1991), DOI: 10.3905/jfi.1991.692347. CrossrefGoogle Scholar
  • J. Lund, Non-linear Kalman Filtering techniques for term structure models. Working Paper, Aarhus School of Business, 1997 . Google Scholar
  • K. V.   Mardia , J. T.   Kent and J. M.   Bibby , Multivariate Analysis ( Academic Press , New York , 1992 ) . Google Scholar
  • C. R. Nelson and A. F. Siegel, Journal of Business 60, 473 (1987). CrossrefGoogle Scholar
  • G. G. Penachi, Review of Financial Studies 4, 53 (1991). Crossref, Web of ScienceGoogle Scholar
  • N. D. Pearson and T. S. Sun, Journal of Finance 49, 1279 (1994), DOI: 10.2307/2329186. Crossref, Web of ScienceGoogle Scholar
  • R.   Rebonato , Interest-Rate Option Models ( Wiley , New York , 1997 ) . Google Scholar
  • G.   Sansone , Orthogonal Functions ( Interscience Publishers , New York , 1959 ) . Google Scholar
  • M. K. Singh, The Journal of Portfolio Management 24, 101 (1997), DOI: 10.3905/jpm.1997.409633. Crossref, Web of ScienceGoogle Scholar
  • L. E. O Svensson, Estimating and interpreting forward interest rates: Sweden 1992–1994. NBER Working Paper, 1994 . Google Scholar
  • O. A. Vasicek, Journal of Financial Economics 5, 177 (1977), DOI: 10.1016/0304-405X(77)90016-2. Crossref, Web of ScienceGoogle Scholar
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