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Extracting factors for interest rate scenarios

Author

Listed:
  • L. Molgedey

    (Institute of Physics, Humboldt-University, Invalidenstr. 110, 10115 Berlin, Germany)

  • E. Galic

    (Allfonds BKG Asset Management, Arabellastr. 27, 81925 München, Germany)

Abstract

Factor based interest rate models are widely used for risk managing purposes, for option pricing and for identifying and capturing yield curve anomalies. The movements of a term structure of interest rates are commonly assumed to be driven by a small number of orthogonal factors such as SHIFT, TWIST and BUTTERFLY (BOW). These factors are usually obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). Although PCA diagonalizes the covariance matrix of either the interest rates or the interest rate changes, it does not use both covariance matrices simultaneously. Furthermore higher linear and nonlinear correlations are neglected. These correlations as well as the mean reverting properties of the interest rates become crucial, if one is interested in a longer time horizon (infrequent hedging or trading). We will show that Independent Component Analysis (ICA) is a more appropriate tool than PCA, since ICA uses the covariance matrix of the interest rates as well as the covariance matrix of the interest rate changes simultaneously. Additionally higher linear and nonlinear correlations may be easily incorporated. The resulting factors are uncorrelated for various time delays, approximately independent but nonorthogonal. This is in contrast to the factors obtained from the PCA, which are orthogonal and uncorrelated for identical times only. Although factors from the ICA are nonorthogonal, it is sufficient to consider only a few factors in order to explain most of the variation in the original data. Finally we will present examples that ICA based hedges outperforms PCA based hedges specifically if the portfolio is sensitive to structural changes of the yield curve.

Suggested Citation

  • L. Molgedey & E. Galic, 2001. "Extracting factors for interest rate scenarios," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 517-522, April.
  • Handle: RePEc:spr:eurphb:v:20:y:2001:i:4:d:10.1007_pl00022986
    DOI: 10.1007/PL00022986
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    Cited by:

    1. repec:hum:wpaper:sfb649dp2007-023 is not listed on IDEAS
    2. Johan Hagenbjörk & Jörgen Blomvall, 2019. "Simulation and evaluation of the distribution of interest rate risk," Computational Management Science, Springer, vol. 16(1), pages 297-327, February.
    3. Borak, Szymon & Härdle, Wolfgang Karl & Mammen, Enno & Park, Byeong U., 2007. "Time series modelling with semiparametric factor dynamics," SFB 649 Discussion Papers 2007-023, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.

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