Update:
I derived a more accurate formula for the hedge ratio, and I will update the arXiv paper accordingly. See the formula below and also a histogram of the hedge p/l in volatility points. I.e. if final value of volatility swap is 20% and the hedge is 20.2%, then p/l is 0.2%.
I ran 500 simulations of the Heston model of daily hedging of a 1 year volatility swap until maturity with variance swap using my formula below for the hedge ratio.
Formula:
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d \mathcal{V}(t) = \frac{1}{ \mathcal{V}(t) + V^2(t) / \mathcal{V}(t)} d V^2(t)
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where [$] \mathcal{V}(t) [$] is the (seasoned) volswap price at time [$] t [$] and [$] V^2(t) [$] is the (seasoned) varswap price at time [$] t [$]. Implication of my paper is that this is robust for practically any SV model.
I am quite happy with this actually. Approximations can be elegant too
The histogram of the PNL:
hedgepnl.png
[img]file:///Users/rallyschwachofer/Desktop/vshedging/hedgepnl.png[/img]