There seem to be two versions of the lognormal Libor in arrears adjustment, one containing exp(variance)-1 as a factor the other only variance instead. Both can be found in papers and books. The former comes from an exact calculation whereas the latter is derived using some approximation as e.g. freezing the drift at t=0. Or, as I now noticed, the latter is in fact the adjustment in a normal black model instead of a lognormal one (see here). In the current low interest rate / high lognormal vol enviroment, the lognormal adjustment may explode and lead to unrealistic adjustments, while the normal adjustment is stable.What is your view on this. My perception so far is that it is rather random which of the two adjustment is implemented in software libs (lucky who has the normal version).

thanks Peter, the topic is very interesting. This is indeed an area which should be looked at (convexity correction in a normal vol world). I'll have a look and revert.K.

In practise the SABR model is used or BGM for non European pay-offs. But this kind of formulas is useful to get a first order intuition and actually can be used for very short maturities and volatilities. But these results are very well know. I would suggest reading the book of Pelsser about convexity adjustment in particular the discussion about the tail dependence which is obviously missed with a normal model. When the variance is very low yes normal is like lognormal with vol_LN times Forward and when the variance is close to zero all the models are equivalents

I agree with ZhuLiAn. The evaluation of convexity adjustments as an expectation on a time-transformed probability measure just isn't that relevant. No matter what model is picked to do that, it is important to decide whether the option skew across the whole strike range is represented by the model. I can tell you that it is not meaningful to use SABR, lognormal or normal across the whole range. Hence, the replication approach with a sensible truncation is just much more meaningful.I think that the approach being discussed here was popular between the mid-1990s to early-2000s. The Dust paper is from 1995, the Pelsser paper from 1999, I think. BTW, just one more thing of market foklore, a normal model in a low rates high vol environment is especially meaningless...

thanks. My point is less that the lognormal or normal adjustment is state of the art (yeah of course it is not...). But in the real world you have many places where these formulas are still in use, at least I have to deal with that. So I found it rather surprising to find these explosions in the simple black model and also the dependency on some arbitrary approximation along the derivation of the adjustment, sometimes done, sometimes not. Said this it seemed important to justify this approximation by some other model which actually produces this adjustment exactly. Most probably this was written down more than once...