Linear Interest Rate Stress Testing with PCA

Discussion on Value-at-Risk Models
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darraghg
Posts: 1
Joined: Wed Sep 30, 2009 9:25 am

Linear Interest Rate Stress Testing with PCA

Postby darraghg » Wed Sep 30, 2009 10:58 am

Hi,
I am working through Example IV.2.9 & 2.10
I can follow the calculation of VaR using the full calculation and using PC

If I understand correctly, the sensitivities of 428, -2,975 and 1,041 are the sensitivities to 1 bp move in the PCs
and the Std Devs are 29, 6, and 3 in bps.

But in terms of stress testing using these PCs, if I apply a shock of 2.33 Std Devs to each component and scale to the holding period, shouldn't I get a similar answer to the VaR calculation?
I can see where the calculations are different, but intuitively if the components are uncorrelated wouldn't you expect the same answer?

Are the two calculations not telling you your expected loss at 2.33 Std Devs?

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Linear Interest Rate Stress Testing with PCA

Postby coalexander » Thu Oct 01, 2009 9:17 am

Hi

Not sure about your use of the term 'stress testing' in this context. I would not call a move to 1% tail value a stress test really...NB these examples are continued to a six-sigma stress test in Ex IV.7.14.

The normal linear PC VaR is 2.33sqrt([b:21nusglq]beta' D beta[/b:21nusglq]) where [b:21nusglq]beta[/b:21nusglq] is PC sensitivity vector (BTW yes, it is sensitivity to 1 bp moves) and [b:21nusglq]D[/b:21nusglq] is diagonal matrix of PC variances. Maybe your question is better phrased as: Can this be rewitten as sqrt([b:21nusglq]beta' E beta[/b:21nusglq]) where [b:21nusglq]E[/b:21nusglq] = (2.33^2)*[b:21nusglq]D[/b:21nusglq] ?

And of course, the answer is yes. So, you are correct, Cheers, C


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