Calculating Variance of a spread using PCA

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sumit_uk1
Posts: 1
Joined: Fri Jun 07, 2013 9:21 am

Calculating Variance of a spread using PCA

Postby sumit_uk1 » Thu Mar 20, 2014 12:39 pm

Hi
I was wondering if its possible to calculate the variance of a spread between 2 spot rates using PCA.

For instance-

1) I do a PCA analysis on my returns (X) which is a Txn matrix
2) I get the Covar matrix V, and the eigen vector W which is a n x n orthogonal matrix. I also get the Eigen values L_i for each of of PCs

If I want to calculate , say : Var(7y - 3y), is it possible to do something like (assuming we consider only first 2 factors:


Var (P&L_ 7y_3y) ~ Var[PV01(7y) * w_1_7y + PV01(7y) * w_2_7y] - Var[PV01(3y) * w_1_3y + PV01(3y) * w_2_3y]

where I have considered only factor 1 & 2 i.e. w1 & w2

Regards;
Sumit

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