I am tasked with delta hedging a variance swap (actually, the replicating portfolio). In theory the delta should be zero, but there is talk of skew delta. I tried computing it using an analytic formula by Coulombe, Marini and Yesaya. The figures I got just did not make sense.Has anyone dealt with this and how does the hedge work?

You are talking about stiicky strike delta, which is delta of integrating Black Scholes calls and puts delta. This only makes if your vega is sticky strike vega. In reality, SPX vols move faster or slower than sticky strike depending on market conditions. Against intuition, if vols indeed are sticky strike, variance swap has zero Black vega exposure and can be completely delta hedged. If your risk system in indeed based on black model, then it should be merely integrating deltas coming from black deltas, but you will need to hedge both delta and vega. On ther other hand, if your system is based on local vol, then your delta is sticky tree delta and your vega is sticky tree vega.

I am referring here to the Demeterfi-Derman-Kamal-Zou paper. In a classical ideal B-S-M world,in terms of trades, if I were to go :- enter a long a 3month variance swap struck at (20%)^2, with variance continuously sampled, from this moment, to hedge it completely, I would need to- short a continuum of calls/puts with 1/strike^2 weights with strike from 0 to +Inf AND continuously delta hedge this option strip AND separately, go a static long 1/S* futures (adjust for the notional amount)1. Is this right?2. The Delta wrt to spot/future of the hedging position ( strip delta-hedged + static long 1/S* ) is NOT 0 (it should be if the pos is to replicate the varswap)3. Is the option strip's delta actually the same as the 1/S* future position, and so I just need to do the delta hedging for the strip?4. If I am long the varswap and short the strip and ..., whatever realized variance turns out to be, I would have 0 P/L (of course in the ideal B-S world) ?regards,