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From my understanding total implied variance has to be a monotonic function of time for there to be no calendar arbitrage. Stumbled upon quotes for this Monday with apparent arb (NKE Dec expiry vs Jan), not sure if this is correct, but I have checked this across open hours and it looks persistent throughout the day.

Is this even possible? Am I missing something?

Vols are derived from mid of top of the book quotes. There are no divs before the expiry.

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  • $\begingroup$ What makes you think implied vol should be monotonic? What you're seeing is commonly referred to as the volatility smile (smirk), it's not an arb opportunity. $\endgroup$ – Chris Oct 29 '20 at 17:31
  • $\begingroup$ where did I saw about vol? $\endgroup$ – sle Oct 29 '20 at 20:12
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    $\begingroup$ I presume you're referring to the higher strikes. Check if you would actuslly have been able to trade it by looking at the vols of the bid and ask. Frequently you'll find arbs in your mid data but not in the bid/ask $\endgroup$ – will Oct 29 '20 at 22:54
  • $\begingroup$ yeah thats it, its not even half tradable with that spread, should have checked this before posting, thx $\endgroup$ – sle Oct 30 '20 at 13:06
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As Will advised to check, there is actually no arb for both put & call considering the spread to be crossed (particularly for Dec expiry) on both legs, ie hitting Dec expiry put wing at bid and lifting Jan at offer.

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