The dynamics of the term structure of interest rates: an Independent Component Analysis

  • Franck Moraux
  • Christophe Villa
Part of the Advances in Computational Management Science book series (AICM, volume 6)


The movements of a term structure of interest rates are commonly assumed to be driven by a small number of uncorrelated factors. Identified to the level, the slope, and the curvature, these factors are routinely obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). In this paper, we focus on the Independent Component Analysis (ICA). The central assumption here is that observed multivariate time series reflect the reaction of a system to some (few) statistically independent time series. The ICA seeks to extract out independent components (ICs) as well as the mixing process. Both ICA and PCA are linear transform of the observed series. But, whereas a PCA obtains uncorrelated (principal) components, ICA provides statistically independent components. In contrast to PCA algorithms that use only second order statistical information, ICA algorithms (like JADE) exploit higher order statistical information for separating the signals. This approach is required when financial data are suspected to be not gaussian.

Key words

Term Structure of Interest Rates Principal Component Analysis Independent Principal Component Analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ané T., Labidi C. (2001), “Implied Volatility Surfaces and Market Activity over Time”, Journal of Economics and Finance, 25 (3), 259–275.CrossRefGoogle Scholar
  2. Bliss R. (1997), “Movements in the term structure of interest rates”, Economic Review, Quarter, 16–33.Google Scholar
  3. Bogner R. (1992), “Blind Separation of Sources”, Technical Report 4559, Defense Research Agency, Malvern.Google Scholar
  4. Cardoso J.-F. (1989), “Source separation using higher order moments”, International Conference on Acoustics, Speech and Signal Processing, 2109–2112.Google Scholar
  5. Cardoso, J.-F. (1999), “High-order contrasts for independent component analysis”, Neural Computation, 11 (1), 157–192.CrossRefGoogle Scholar
  6. Cardoso J.-F., Souloumiac A. (1993), “Blind beamforming for non-Gaussian signals”, IEE Proc. F., 140 (6), 771–774.Google Scholar
  7. Chaumeton L., Connor G., Curds R. (1996), “A Global Stock and Bond Model”’, Financial Analysts Journal, 52 (6), 65–74.CrossRefGoogle Scholar
  8. Comon P. (1994). “Independent component analysis a new concept?”, Signal Processing, 36 (3), 287–314.CrossRefGoogle Scholar
  9. Jamshidian, Farshid, Yu Zhu (1996), “Scenario Simulation Model: Theory and Methodology”, mimeo, Sakura Global Capital.Google Scholar
  10. Kahn R. (1989), “Risk and Return in the U.S. Bond Market: A Multifactor Approach”, in Fabozzi F. (ed.), Advances & Innovations in the Bond and Mortgage Markets (Probus).Google Scholar
  11. Kambhu J., Rodrigues A. (1997), “Stress Tests and Portfolio Composition”, mimeo, Federal Reserve Bank of New York.Google Scholar
  12. Knez P., Litterman R., Scheinkman J. (1994), “Explorations into Factors Explaining Money Market Returns”, The Journal of Finance, XLIX (5), 1861–1882.Google Scholar
  13. Litterman R., Iben T. (1991), “Corporate Bond Valuation and the Term Structure of Credit Spreads”, The Journal of Portfolio Management, Spring, 52–64.Google Scholar
  14. Litterman R., Scheinkman J. (1991), “Common Factors Affecting Bond Returns”, The Journal of Fixed Income, June, 54–61.Google Scholar
  15. Loretan M. (1996), “Market Risk Scenarios and Principal Components Analysis: Methodological and Empirical Considerations”, mimeo, Board of Governors of the Federal Reserve.Google Scholar
  16. Murphy B., Won D. (1995), “Valuation and Risk Analysis of International Bonds”, in Fabozzi F., Fabozzi T. (eds.), The Handbook of Fixed Income Securities, New York, Irwin.Google Scholar
  17. Murphy K. (1992), “J.P. Morgan Term Structure Model”, mimeo, Bond Index Group, J.P. Morgan Securities, Inc.Google Scholar
  18. Oja E. (1989), “Neural networks, principal components and subspaces”, International Journal of Neural Systems, 1, 61–68.CrossRefGoogle Scholar
  19. Pope K., Bogner R. (1994), “Blind separation of speech signals”, Proc. of the Fifth Australian Int. Conf. on Speech Science and Technology, Perth, 46–50.Google Scholar
  20. Tong L., Liu R., Soon V., Huang Y. (1991), “Indeterminacy and identifiability of blind identification”, IEEE Trans. Circuits Systems, 38 (5), 499–509.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Franck Moraux
    • 1
  • Christophe Villa
    • 2
  1. 1.CREREGUniversité of Rennes 1France
  2. 2.CREST — ENSAI and CREREGUniversity of Rennes 1France

Personalised recommendations