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Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol.

Why?

I must be missing something obvious.

---Update---

Finally got a response in terms of more documentation, and a half sentence that mentions lognormal vs normal, which I'm assuming means they are saying that the cap vol is a Black (i.e. lognormal) volatility of dr/r, but we want a normal volatility for the Hull-White model of dr (which they use). So multiply by r both sides.

Which is, I suppose, approximately the right idea? Except why the 10y cap vol and 10y rate, when the Hull-White model is a one-factor model of the short rate; the 10y rate is not the short rate, even if we assume the volatility is constant and equal to the value at 10y.

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Maybe ask Bloomberg? –  Joshua Ulrich Feb 11 at 14:28
    
It's too much for their customer service people; producing the document that I got that formula from is all they can do. –  Phil H Feb 11 at 14:29
    
You mean it's not in their manual of scripts?!? :) I meant: call your Bloomberg representative. –  Joshua Ulrich Feb 11 at 14:32
    
That doesn't sound right, definitely help help that and escalate until you get a better answer. –  experquisite Feb 11 at 19:46

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