Is there a link between those two quantities ? I think about this because, the skew of returns impacts the price of calls and puts, and therefore may be linked to the implied volatility
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$\begingroup$ With skew of returns I presume you mean the skewness of retuns, which is the third (centralized) moment of returns. In that case the answer is yes. One of the earliest papers relating IV skew to skewness of retuns is Backus et al, Accounting for biases in Black-Scholes, 2004. $\endgroup$– user34971Dec 1, 2021 at 14:23
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$\begingroup$ Yes that is what I meant ( I corrected the title), thanks for the paper, I'll check it out. The question is raised because I am quoting new options on the market and so far, with the little data we have on this newborn option, only ATM options prices are satisfactory ; the skew for the implied volatility we created is mapped to a reference product implied volatility but the skew does not seem good so we are looking for a way to map the skew better. $\endgroup$– KupocDec 1, 2021 at 14:37
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$\begingroup$ There is a link, just as you intuit. Common ways people have tried to take advantage of it include Edgeworth expansions and similar tricks. Here is a paper: tandfonline.com/doi/full/10.1080/1331677X.2018.1530607 $\endgroup$– Brian BDec 1, 2021 at 21:55
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$\begingroup$ Thanks for the paper, it is pretty similar to the one @FridoRolloos mentioned earlier. $\endgroup$– KupocDec 2, 2021 at 13:56
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