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amoskoh
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Joined: May 19th, 2011, 3:19 pm

Results of PCA on Yield Curve vs Forward rates for estimating HJM volatilities

August 13th, 2018, 9:47 am

I tried performing PCA on two sets of data
A) USD swap rates 1Y up to 30Y
B) Implied forward rates (half yearly maturities up to 30Y) from the yield curves in A

Some observations
- the classical level/slope/curvature shape on the first three eigenvectors is more pronounced in A compared to B 
- PCA on forward rates are very sensitive to my method of interpolation and the eigenvectors have jagged lines
- the first three factors in A have higher cumulative variance than B  (98% vs 92%)

Some questions with regards to using the results 
1) Are my results typical (where using forward rates, there tends to be higher distortion to level/slope/curvature) 
2) Is it common to apply some adjustments on the forwards for it to look more like PCA on the yield curves with clear level/slope/curvature before using it in the HJM model.. those jagged lines don't look too great
2) Else.... Is there a way to convert the PCA results on yield curves into the volatilities for the HJM model to retain the good level/slope/curvature
 
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bearish
Posts: 5906
Joined: February 3rd, 2011, 2:19 pm

Re: Results of PCA on Yield Curve vs Forward rates for estimating HJM volatilities

August 13th, 2018, 4:38 pm

I think your results are pretty typical. But, assuming that you are using data from the last decade, you should certainly not expect the nice level, slope, curvature PCs you find in data from the 90’s. With long maturity rates being far more volatile than (central bank pegged) short rates, the first PC will have a significant slope component. That will then require a richer shape to the second PC (to be orthogonal to the first one) and so on. You can try to smooth your forward PCs directly, and check that you are not doing anything crazy by regenerating the covariance matrix from the smoothed PCs.