A paper (hopefully one of my last on volswaps!) on robust hedging of volswaps using varswaps only. I think that would make the hedging of volswaps more feasible than continuously rebalancing a strip of options.
questions and comments welcome.
https://arxiv.org/abs/2001.02404
nonparametric hedging of volswaps with varswaps
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frolloos
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nonparametric hedging of volswaps with varswaps
No vanna, no cry
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frolloos
- Posts: 0
- Joined: Thu Jan 01, 2004 12:00 am
nonparametric hedging of volswaps with varswaps
Update:
I have actually derived a more accurate formula for the hedge ratio (i.e. the number of varswaps to hold to hedge 1 volswap), and I will update my arXiv paper shortly. But here is the formula for the impatient:
[img]/User%20Files/3969/formula.png[/img]
where K_{vol} is the seasoned volswap price and K_{var} is the seasoned varswap price. The seasoned volswap price can be derived from the observable smile in a model-free manner as detailed in the paper.
Now here is I think the nice part. I ran, under the Heston model, 500 simulations of daily hedging of a 1 year volswap with a varswap according to my formula above, and the histogram below shows that it is quite accurate. What I mean with a hedge pnl of say .2% is that the terminal value of the volswap is 20% and the hedge value is 20.2%.
For Kvol I used the exact Heston value for now, because I first wanted to test the hedge formula, and I am confident it is good now. If using my model-free approx for Kvol then the hedge pnl result will of course be less accurate as below but I think still quite good.
Hopefully, in addition to winning myself a nobel prize in approximations, this stuff can start to give more liquidity in volswaps.
Will post when arXiv paper has been updated with the formula and numerical results.
[img]/User%20Files/3969/hedgepnl.png[/img]
I have actually derived a more accurate formula for the hedge ratio (i.e. the number of varswaps to hold to hedge 1 volswap), and I will update my arXiv paper shortly. But here is the formula for the impatient:
[img]/User%20Files/3969/formula.png[/img]
where K_{vol} is the seasoned volswap price and K_{var} is the seasoned varswap price. The seasoned volswap price can be derived from the observable smile in a model-free manner as detailed in the paper.
Now here is I think the nice part. I ran, under the Heston model, 500 simulations of daily hedging of a 1 year volswap with a varswap according to my formula above, and the histogram below shows that it is quite accurate. What I mean with a hedge pnl of say .2% is that the terminal value of the volswap is 20% and the hedge value is 20.2%.
For Kvol I used the exact Heston value for now, because I first wanted to test the hedge formula, and I am confident it is good now. If using my model-free approx for Kvol then the hedge pnl result will of course be less accurate as below but I think still quite good.
Hopefully, in addition to winning myself a nobel prize in approximations, this stuff can start to give more liquidity in volswaps.
Will post when arXiv paper has been updated with the formula and numerical results.
[img]/User%20Files/3969/hedgepnl.png[/img]
No vanna, no cry