I'm working on a project to justify the use the certain tenors (2y, 5y, 10y, 30y) for risk bucketing. I'm a little stuck after calculating the principal components. Just to describe my approach-
a) Got the GBP swap rates for 1y - 60y for 2 years of historical data (Let's say X matrix).
b) Calculated the daily differences and then the correlation matrix
c) Calculated the eigen values and eigen vector matrix (say A)
d) To get back the PC rates Y (say, PC01, PC02,...PC60), I did a matrix multiplication of demeaned X matrix and eigen vectors (say, X_dm and A)
e) Plotted PC01, PC02 and PC03 and the shape confirmed what is expected for the level, slope and curvature
f) From what I had read in an article, if I plotted PC01 against 5y or 10y swap rate, they would mostly be following the same pattern. However, this is something I couldn't confirm. (Providing a link of the article)
So my question is how do I prove that the use of 2y, 5y, 10y and 30y is justified for risk bucketing and not other alternate buckets?
Unfortunately, since I'm working on this from my office, I can't paste any figures/charts I have generated.
Articles referred - https://www.garp.org/#!/risk-intelligence/all/all/a1Z1W000003rQUYUA2
https://www.clarusft.com/principal-component-analysis-of-the-swap-curve-an-introduction/
One more question - if anyone goes through the GARP article, how is the figure 2 actually generated? Any ideas?
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