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