# Volatility swap hedge

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?

I am aware of but have not yet read through Peter Carr and Roger Lee's paper Robust Replication of Volatility Derivatives. Please do reiterate the points you think is essential from that paper.

• Well, if you have options, you can seemingly come up with a position which has zero delta to price changes, but would change in value if $\frac{d\sigma}{dt}$ changes alone. That's not a complete answer, but it seems a good start. – eSurfsnake Apr 8 '18 at 4:19
• @eSurfsnake: Are you just delta-hedging an option but leaving the volatility unhedged? Is that not beside the point of hedging the volatility swap which calls for hedging the volatility? – Hans Apr 8 '18 at 6:31
• A major result in the literature is that: a varswap can be hedged with a static option position plus a dynamc position in the underlying, a volswap hedge requires a dynamic position in options (which makes it very inconvenient and costly to hedge a volswap). Read the paper by Carr thoroughly. – Alex C Apr 8 '18 at 11:35
• @AlexC: Thanks. I am already aware of Carr & Lee's paper, as I have already mentioned in my question. I would appreciate it if you can comment on the practicality of applying the approach in that paper or other papers to a vol swap not a variance swap, specifically to hedge away the convexity adjustment. – Hans Apr 9 '18 at 0:39

Here is a practical hedge for forward volatility swaps using only straddles with a certain strike, and with a notional that is determined by the skew at that magic strike. The same method for spot/seasoned volatility swaps will be posted online in due course as well.

Frido Rolloos, Model-Free Pricing and Hedging of Forward Starting Volatility Swaps.

• The link is broke. Could you please put the title and author on as well as the updated link? Thank you very much. – Hans Jan 9 at 14:20
• @Hans Thanks - I have merged two papers into one, so the new link to the paper on forward starting volswaps is papers.ssrn.com/sol3/papers.cfm?abstract_id=3177299 and the link for plain volswaps is the arXiv paper link I posted below. – ilovevolatility Jan 9 at 14:24

Apologies for the delay on the hedging of non-forward-starting volatility swaps, but it's only since this week that I have an answer for this.

So, for plain volswaps, I can give you a nonparametric hedge in terms of varswaps only. That's not as cheap as using a single option (which I believe is not possibe anyway), but certainly better than trading an infinite number of options.

Nonparametric, as you know, meaning the hedge ratio does not depend on the particular SV model, i.e. model independent.

The link below gives the hedge. My contact details are at the bottom of the title page if you have questions.

Nonparametric Hedging of Volatility Swaps with Variance Swaps in StochasticVolatility Models by Frido Rolloos.

EDIT:

Please note that the paper has been updated (same link) with a more accurate and novel hedging formula and numerical simulations. Below is one chart of hedging error taken from the paper. A hedge P&L of say -0.3% means that the difference between the replicating portfolio / hedge and the terminal realised volatility is for instance 19.7% - 20% = 0.3%.

• +1 Thank you, very much! Let me read your paper. – Hans Jan 9 at 14:18
• Thank you so much for the update! Embarrassingly, I have yet to read your paper, but is of high priority on my to-do-list! I will give feed-back afterwards. – Hans Jan 20 at 18:59
• @Hans No worries, take your time of course. If you also carry out your own numerical experiments based on results in the paper I'd be very interested in your findings as well. Always good to know when/where a model or approximation works well and when/where it doesn't. – ilovevolatility Jan 21 at 6:43