In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under the BSM framework.
My question is for the former case. Let's assume the option IV is 20% and the true future volatility is 30%. We buy the option at 20% IV and delta hedge using 20% IV. As we move forward in time, if the option that we bought has an IV that changes, let's say now it is at 25% IV. Do we now delta hedge at 25% IV or do we continue to hedge at 20% IV? The literature never makes this part clear.