Delta-Hedging and Variance Swap Replication

Papers treating variance swap replication often mention that the replicating portfolio consists of a static position in an appropriately weighted continuous strip of options, and a dynamic position in the underlying asset that can be regarded as the delta-hedge of the strip of options. Most papers, however, do not explicate the impact of delta-hedging the options, and in particular do not mention what volatility to use when delta-hedging the options. Although no new results are derived, in this educational note we clarify the aforementioned two points.