I am implementing a convexity adjustment routine using HJM for the futures curve. I am unsure if this question is extremely basic, but I always get confused when it comes to choosing the appropriate volatility to fit the model.

Which volatility do I have to use to do a convexity adjustment? Can I use cap/floor implied vols to do this or is this the wrong approach? Are there alternatives?

I might be wrong, but I believe cap/floor vols are commonly used...

Ok thanks, that will have to do. For some reason I do not see this as an intuitive approach, but this might be mainly because I can't see beyond "straight-forward" applications of cap/floor implied vols. 

As a sanity check, it is also a good idea to try and tie out the resulting curve to the corresponding swap rates. If your calibrated model suggests that you can make material profit by arbing futures against swaps, I'd consider an adjustment to the calibration.

In addition to what bearish mentioned, you could use BBG's numbers (based on Hull-White) as a sense-check...

Ok thanks very much to both (@bearish and @martinghoul). To my surprise, I have also found out that some people use BS implied cap vols to plug into the HJM convexity adjustment formula. Since these vols are model-dependent, I wonder how this can work at all since I'd be essentially using vols generated from one model and putting them into a different one. 

Do you have a better approach?  IMHO, everything in the world of futures convexity adjustments is sorta philosophical nowadays.  Not even sure the concept has the same validity any more, tbh.

Hi, using eurodollar option volatilities is preferable, obviously, for consistency reasons. But in practice cap/floor vols are fine, as it is often the case that these vols are marked off of eurodollar vols anyway. The vol surface is often a hodge podge in that area, but if you are careful about this, this is where a lot of the money is in that space.

There is not much point going crazy with modeling the adjustment, although it does make sense to bring in some skew and correlations. Hence a skew BGM model is good for this. The problem with eurodollar convexity is that it's not really a textbook case about the futures variation margin, but more complex than that.

As often, I don't agree with bearish, who might be sitting too far away from the desk too deeply involved in studying written quant finance. That is what quants do I guess  

 

Note that if you use Black cap / floor vols you must multiply them by the swap rate with the same maturity to get an approximation of a normal volatility (because HW is a normal model). Or you can input directly a normal vol.