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There are only quarterly contracts (3,6,9,12) for SX5E futures. In practice, how do we hedge SX5E option at expiry for non-quarterly contracts (say April)?

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This is just like any other option. For example, if you are trading an IBM option, you hedge with IBM stock, which doesn't expire at all, (obviously).

You then sell your hedge in the gamma-storm that enuses at expiry.

For longer term options where you have an expiry that goes way past the futures you have two choices:

  1. Trade the rolls periodically and/or
  2. Exchange some of your delta into longer term swaps
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  • $\begingroup$ The fundamental difference between SX5E and IBM is that IBM option are physically settled. So if I long 1 ITM IBM option and short 100 IBM stocks before expiry, then I am still delta neutral after expiry. But SX5E is cash settled. $\endgroup$
    – MainCom
    Apr 14 '21 at 14:47
  • $\begingroup$ Remember, with regular contracts your delta on't be equal to your shares. You might have 1 contract long IBM hedged by 50 shares short of IBM. As you get to expiry, the gamma is going to move wildly as you approach the final moment. You have to trade up to the 100 shares of IBM or get rid of the 50 shares. $\endgroup$
    – JoshK
    Apr 14 '21 at 15:05
  • $\begingroup$ Also, to get help get rid of the delta people will trade the "SQ" in cash. That would mean selling or buying the basket of stocks on the expiry print. So you can hedge some of the delta that way and EFP to close. $\endgroup$
    – JoshK
    Apr 14 '21 at 15:06
  • $\begingroup$ That's not what I concern. I 'continuously' hedge the option, so the delta of the position will be zero before expiry if it is ITM and not to close to the strike. $\endgroup$
    – MainCom
    Apr 14 '21 at 15:08
  • $\begingroup$ Oh, I see what you are saying. So if you are worried about the fact that you don't have a physical to offset your hedge (derriv), you have to trade the SQ, right? You'll have setting risk otherwise. $\endgroup$
    – JoshK
    Apr 14 '21 at 15:11

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