I have a simple question concerning the computation of Convexity Adjustment in case we are using a stochastic volatility model (SABR dynamics) to price a CMS Cap. If we choose to price the CMS Cap using Black76 (constant vol) we simply apply Hull?s formula for Convexity Adjustment to every FWD rate of every Caplet. This is fairly straight.If we use stochastic volatility (SABR dynamics) we have to use an alternative way to compute Convexity Adjustment (to incorporate the smile). After studding the relative literature, and threats in this forum, I concluded that we have the two following alternatives.? Calculate the Convexity Adjustment using Put - Call parity, and replicating Cap and Floor with Swaptions.? Use Merurio?s formula for Convexity Adjustment, which is at the paper ?Swaption skews and convexity adjsustments? (page 6).The problem with the first approach is that (although accurate and straight) it is extremely computational expensive. The problem with the second approach is that for large expiries the integral is not converging, and its price depends from the upper limit. Question: Are the above accurate? If yes does anyone has anything to suggest overcoming this two problems? I am a practitioner so I would really welcome any comments.Thank you all very much in advance.

Have not seen this threat: SABR approximations - best practice?