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It is known that a variance swap can be replicated by a strip of options. However, it is costly to trade that many OTM options and there is not enough liquidity to trade the wings in the quantity that is necessary. So I suppose banks do not actually trade the entire strip. The question is then, how do they hedge this position? Do they hedge the BS delta of the variance swap and trade a 25d put against it or something similar?

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    $\begingroup$ Does JPM, section 2. Valuation and Hedging in Pratice help? Also, the practical difficulties in replicating the actual log payout across strikes, is the reason that the market for equity index varswaps usually trades at a basis to the replicating portfolio. $\endgroup$
    – AKdemy
    Mar 24, 2023 at 0:01
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    $\begingroup$ It is more or less as @AKdemy wrote. I used to trade varswaps as a buyside ptf.mgr. There was always a basis especially for longer tenors. This basis could be attributed to the impact of interest rates (can't take them to be deterministic anymore for longer dated), but especially the fact you replicate only up to a certain strike. I am not aware of an easy way to calculate this basis, but one way could be: simulate the payoffs of the discrete replicating portfolio and calc the mismatch wrt to the continuous replicating portfolio. Add the mean of this difference to the price. $\endgroup$
    – Frido
    Mar 24, 2023 at 6:59
  • $\begingroup$ @Frido, I am interested in reading more about that - i.e. how how the pricing is done in practice and the differences to the theoretical continuous replicating portfolio price. Any resources you can think off? $\endgroup$
    – phdstudent
    Mar 24, 2023 at 14:43
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    $\begingroup$ @phdstudent Well there is this open access paper, and references therein might be relevant as well. I haven't spent much time on this yet to be honest, but it's an interesting and practically relevant subject: mdpi.com/1911-8074/11/1/11 $\endgroup$
    – Frido
    Mar 24, 2023 at 15:19
  • $\begingroup$ @Frido It is not the pricing I am discussing though. I am more interested in how dealers hedge the exposure to the variance swap knowing that they will not trade the entire strip against it. $\endgroup$
    – Rodrigo
    Mar 24, 2023 at 17:29

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