I’m working on an implementation of In-Arrears-Libor options (Caps, floors etc.) To do that I’m using the convexity adjustment specified in Brigo & Mercuri, where the Black ’76 model is used to model the forward rate. The implementation is done quit easy, but my problem is what volatility to use? I’m using a SABR model to find the forward volatility, but what strikerate should be used?The In-Arrears-Caplet formula can be split up in valuing a Black ’76 part and a convexity correction part. For the first part I should use the volatility for the strikerate for the cap, but what about the last part? If I want to check my prices using the put-call-parity, I believe there should be some consistency between In-Arrears-Caps/Floors/Swaps, so if I use the ATM volatility for the In-Arreas-Swap convexity adjustment I should also use the ATM volatility for the convexity adjustment for caplets and floorlets. Is this correct?

Have a look at Hagan's paper in wilmott magazine, "Convexity conundrums:CMS Swaps, Caps and floors", it answers this question in the case of CMS index. ATM vol for swap, vol at the strike for out of the money options, then put-call parity for in the money options. You can also compare this approach to full replication across the smile.