Hi All, 

I have read through Pat Hagan's article (http://www.javaquant.net/papers/ConvexityConundrum.pdf) as well as Fabio Mercurio's articule on CMS convexity adjustment (http://www.fabiomercurio.it/sabrcms.pdf). However, I have difficulties connecting the arguments stated in each article. I truly appreciate any experts could help me out here. 

I have been told that a simple caplet can be replicated by a series of payer swaptions with adjusted notional amount. However, in Fabio's paper, it mentioned the CMS "Rate" can be replicated by a series of payer swaptions. I have a hard time in connecting these two argument. It looks like the CMS Rate needs a convexity adjustment which is equal to a series of payer swaption. Then we can just the black model to price it. Or the other way is we value the CMS caplet using a series of payer swaption. How should I connect these two methodology? 

Thanks for your help! 

Seahawk