Is this to hedge the corresponding variance swap? Could you please elaborate on what you mean by "buy/sell the entire surface" -- by "surface" I suppose you mean the implied volatility surface, right? --- and what you mean by "trading the different delta with inverse weights to their moneyness", and why the former implies the latter?Ideally you need to buy/sell the entire surface (hence, trading the different delta with inverse weights to their moneyness)
I suppose this confirms my speculation that your previous description applies to the corresponding variance swap.but that would expose you to convexity, which you will not be compensated with the vol swap.
Are you saying people essentially leave the convexity risk unhedged, putting in the risk pool notwithstanding?In practice the market makers either put the risk in their risk pool or replicate with vanillas and bear the convexity cost.
What do you mean by "fixing" and "hedging the delta"? By the latter, do you mean hedging the delta of a vanilla option?When it comes to hedging the delta between the fixing it's rather simple calculation.
Carr & Lee's approach is (almost) model free and from that perspective useful. But it's only an approximation to the volswap strike (correlation immune to first order). I don't think it's possible to have a full model free expression for the volswap strike. It's easy to see for example that the volswap strike under local volatility would be different than volswap under stochastic volatility.What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging?
Thank you very much for introducing me to the PDE approach and the references thereof. I will look into it. I am more interested in the vol swap with the volatility [$]\sigma[$] described by the so called inverse gamma processCarr & Lee's approach is (almost) model free and from that perspective useful. But it's only an approximation to the volswap strike (correlation immune to first order). I don't think it's possible to have a full model free expression for the volswap strike. It's easy to see for example that the volswap strike under local volatility would be different than volswap under stochastic volatility.What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging?
The PDE approach is more flexible and has my preference. Google for instance Broadie & Jain volatility derivatives, or Javaheri, Haug, Wilmott Garch and volatility swaps to see how the PDE method works for vol derivatives. Broadie and Jain applied it to Heston model, the other paper to GARCH, but the PDE approach can be used for any model (eg local vol, LSV etc).
The PDE approach should also give you the correct hedge ratios, i.e. the number of variance swaps to use to hedge the volswap MtM.
Another approach would be to specify a model for the variance strike curve. Then you could have options on variance, and if you have those you could "easily" replicate the volswap using a strip of variance options.
Hope that helps.
Check out this post on consistent valuation and risk management of vol derivatives and vanilla options:What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging?
That looks interesting. Is there a technical paper on your valuation and risk mgt method or is it proprietary?Check out this post on consistent valuation and risk management of vol derivatives and vanilla options:What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging?
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