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If all of the other inputs into black scholes (divs/rates/time to maturity/strick/current price/etc) are all the same between two pairs of calls/put contracts on the same security, shouldn't the implied volatility be the same?

For example I see SPY and AAPL has having similar IV for ATM put and calls.

However, it seems like for NFLX and GME, the calls have slightly higher IV? Why is that? In some cases, I have seen the ATM puts command a higher premium (embedded financing cost of shorts, but why is the IV sometimes lower for those puts?)

December 17th monthly option for SPY/AAPL/GME/NFLX

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    $\begingroup$ There is no put-call parity for American options $\endgroup$
    – Ivan
    Commented Dec 2, 2021 at 2:06
  • $\begingroup$ @Ivan there is only put call parity for european options when you only take into account the value of the option. After you include margin requirements, then if you have a difference in funding cost to the interest rates the exchange pay you on margin then you have a different value for the option + margin for calls and puts if the exchange requires differnt margin amounts for ITM and OTM options, $\endgroup$
    – will
    Commented May 2, 2022 at 10:36

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Firstly, there is no put call parity for American exercise as Ivan notes, but parity can provide bounds

But for European options, The IVs are the same for calls and puts at the ATM forward strike. The IVs will not be the same for ATM spot unless the forward equals spot. For stocks with very high dividends and/or borrowing costs, the forward price can be very different than the spot.

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  • $\begingroup$ Why wouldn't the IV, for european options, be the same for ATM spots? Shouldn't that hold no matter the strike? $\endgroup$
    – KT8
    Commented Dec 3, 2021 at 20:32
  • $\begingroup$ Theoretically the IV for European options with same strike should be the same. It’s possible they differ slightly due to the transaction costs of performing the arbitrage. Eg if you were to sell the call / buy the put, you would have to get long the forward stock which may be at a different price than in your model. $\endgroup$
    – dm63
    Commented Jan 2, 2022 at 18:31

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