I get this question a lot in DMs so putting it here so I can refer to it later. "Why do put options and call options at the same strike have different implied volatilities (attaches screenshot of broker GUI)?"
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its not skew


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So what ought to happen to BS IV of an ATM call, priced using implied forwards, as a biggish dividend approaches… nothing? Because all of the effect is captured by the forwards on the premise that everyone must exercise?
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SPX index option calls and puts which are European and cash-settled on expiry show diff ImplVols on TOS SOMETIMES.
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Yup. When you take into account the dividend and borrow there will be no synthetic arb as some people believe like a conversion/reversal on the same strike. Too many people thought this was possible GME and AMC.
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How you compute implied forward/vol for American options on div paying underliers gets a bit more complicated because call/put parity doesn’t exactly, but the logic is the same. A kink in the vol surface for a given term means implied forward is wrong.
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Idk if this is used in the options T&S but thinkorswim, which is what this whole thing was based around iirc, uses Bjerksund-Stensland rather than BSM, at least on the Risk Profile area
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I really doubt it takes into account borrow fees though
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