Is there a paper that explicitly shows/demonstrates that a variance swap can be replicated by delta-hedging a strip of options?

Thus far I have not found anything: papers mention it in passing sometimes, but never really demonstrate this.


Well, I still haven't found any paper/note that shows what I was looking for, so I decided to write it up myself for my own benefit, and maybe also for others:

Delta-hedging and variance swap replication

  • $\begingroup$ There are loads, ie wilmott, and jpm as two examples. $\endgroup$
    – will
    Aug 24 '19 at 14:17
  • $\begingroup$ Those discuss the delta hedge p/l of a single option, but don't show explicitly that delta hedging the entire strip gives the varswap. In particular none of these papers or others afaik show that the hedging implied volatility is irrelevant as long as you hedge all the options using a constant hedge volatility (which is not hard to prove I think) $\endgroup$ Aug 24 '19 at 14:26
  • $\begingroup$ It's pretty easy to understand - the portfolio of options matches the Greeks of the varswap, but it picks up a delta each day which the varswap loses on each fixing. The delta hedging is just to match the delta each day, it's from the same argument that gives you the portfolio in the first place, you're just dealing with the delta it picks up in time. $\endgroup$
    – will
    Aug 24 '19 at 15:12

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