Wanted to ask if a single or different volatilities should be used in Reiner-Rubinstein's option barrier pricing formulas given the following:
An Up-and-out call (Cuo) with strike K and barrier H is valued as Cuo = C - Cui where C is a plain vanilla call with strike K and Cui is an up-and-in barrier call.
The first part of the Cdi formula is a plain vanilla call with strike H. Since volatility values extracted from implied volatility surfaces are dependent on maturity and strike, K and H will yield different volatilities.
Should the two different volatility values be used, one for C and one for Cui? If so, which volatility is to be used for the rest of the terms of the formula for Cui? Which approach is possibly favored by market participants?