Hedging Volatility Swaps with Options and Rebalancing
Summary
The document explains why a single straddle can be a starting point for hedging a volatility swap but is generally insufficient once realized volatility evolves. A more robust replication approach uses a strip of options that is continuously rebalanced. The cited work aims to make the hedge approximately valid across a broad class of stochastic volatility models, without relying on one specific model.
For a hedge using only one option, the suggested method is to choose a model, simulate the sensitivity of both the option and the volatility swap to instantaneous volatility, and select a notional that matches those sensitivities. This can reduce trading costs relative to rebalancing a strip, but makes the result model-dependent and still approximate. The discussion distinguishes volatility swaps from variance swaps, but offers no derivation, numerical example, or detailed comparison of hedge performance.
Key ideas
- A straddle may provide an initial hedge for a volatility swap, but one option alone will not generally remain adequate as realized volatility changes.
- Continuously rebalanced strips of options can provide approximate replication across many stochastic volatility models.
- A single-option hedge can be sized by matching simulated sensitivities under a chosen model.
- The single-option approach can reduce transaction costs but introduces model risk and remains approximate.
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Full text
# Volatility swaps hedging # Volatility swaps hedging I have heard that traders use a straddle to hedge volatility swaps (in the FX context), although I could not figure out the specifics. Is this type of hedge used in practice? And if yes, how does it work? Is there an approximation formula that could be written down to justify such a hedging strategy? This is a question about VOLATILITY swaps, not variance swaps. ## Answer by Frido (score 3, accepted) https://quant.stackexchange.com/a/74370 EDIT: In my answer below I mentioned that to hedge with an option of one particular strike only you need to choose a model. I just posted a short paper that explains how to do this without actually knowing the model. The price paid for this parameter-free hedge is that it is not exact, but an approximation. Here is the paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5001434 Although this question seems Taylor-made for me, I shall resist promoting my own work and refer you instead to Carr and Lee's seminal paper Robust replication of volatility derivatives. Basically what the paper demonstrates is that although initially you could start with a simple straddle (ATM is not always the best choice, but that's another matter), once there is realised volatility a single straddle won't do. To replicate the volswap you'll need to continuously rebalance a strip of options whether you follow Carr and Lee's or my method. The reason the aforementioned methods use a continuously rebalanced strip of options is because they try to be as model-free as possible, ie to be approximately right for a very large class of stochastic volatility models. Hence, if you only want to use single options to hedge a volswap, your best route would be to choose a particular model, do a numerical simulation to calculate the sensitivity of a particular option and the volswap to the instantaneous volatility, and match these sensitivities by choosing an appropriate notional for the option. In this case you could think you're exactly right, but then you are exposed to model-risk and so you're still only approximately right. But at least you save on transaction costs. Hope this helps.
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