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is there a (simplistic?) formula to convert spot risk PV01 into the forward risk PV01?

For example, if I have a

a) PV01 spot risk : 1yr = 100k/bp, 2yr = 50k/bp, 3yr = 25k/bp

b) how can I project this into the forward risk seen from 0 to 1yr (? k/bp), 1yr to 2yr (? k/bp) and 2y to 3yr (? k/bp)

Kind regards

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  • $\begingroup$ I'm not sure what you mean by forward PV01. The PV01 is the present value of 1 basis point. Could you be talking about DV01 (dollar value of the change of 1 basis point in market rates)? $\endgroup$ – David Duarte Jan 24 '20 at 15:15
  • $\begingroup$ nope. I meant the forward rates and forward risks. FRAs and IR futures are can be matched to the ECB meetin dates and decisions. Markets trade them, and it makes more sense to see the risks in the forward space. However, main risk pricing engine has to collate all traded instruments including EONIA swaps and IR swaps which are spot-starting $\endgroup$ – Kiann Jan 24 '20 at 18:00
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Yes. Ignoring discounting, you can say the following:

25k 3yr spot = 8.3k (0y to 1y)+ 8.3k (1yto2y) +8.3k (2y to 3y)

50k 2yr spot = 25k (0y to 1y )+ 25k (1y to 2y)

100k 1yr spot = 100k (0yto 1y)

Adding, we have 133.3k (0y to 1y)+ 33.3k (1yto2y) + 8.3k (2y to 3y)

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