Components of yield curve movements

thumbnail of componentsofyieldcurve Original by R.Franlkland, E. Biffis, D. Dullaway, S. Eshun, A. Holtham, A.D. Simith, E. Varnell, T. Wilkins, 2008, 22 pages 

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Illustrative worked examples, An interim report for the stress test working party, finance, investment and risk management convention (draft working paper)
  • Considers to decompose yield curve into components: polynomial, principal components and variance matching
  • Decompose into components:
    • first component = level of yield curve
    • second component = slope
    • third component = curvature
  • Do not use Polynomial on t as it has tendency to to converge to infinity with large t (while yield curve tend to flat out)
  • Principal component analysis (PCA) by Anderson 157 is devised so that the early components (Z1 ans Z1) explain as much as possible the variability in rates
  • Because of its simplicity, use Cholesky decomposition as the preferred algorithm for Monte Carlo work
  • Consider lower the number of components
  • Analysis performed showed 6 components at most were necessary
  • Variance matching:
    • One factor model
    • 3 factor variance match
    • 3 factor models using alternative weightings
  • Variance matching advantages
    • replication of yield variance, variance of the first and second differences
    • avoids the need to specify time weights
  • Variance disadvantages
    • inability to build to add more factors incrementally (PCA better for that)
    • tendency to wiggle, less intuitive than with a second factor relating slope and a third factor curvature