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I wanted to know what one should be aware of trying to fit volatility smile. Besides the arbitrage issues. What are some of the real life vexing issues associated with this process.

What is a non-parametric smile?

Thanks in Advance,

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    $\begingroup$ Something that people always get wrong is really simple - the forward. If you get the forward wrong you'll get different vols for puts and calls. Fixing thst by just using the otm options is not a fix and just hides the issue. $\endgroup$ – will Oct 26 '19 at 11:51
  • $\begingroup$ Thank you for your response. The index options are European, hence one can possibly use PCP to infer the forward using ATM options. Again the forward has to be consistent across the smile. Is that a problem? However, what do people do for American options? $\endgroup$ – Ramesh Kadambi Oct 26 '19 at 12:49
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    $\begingroup$ this is the kind of assumption that causes issues. You don't have mid prices, you have bid/offers, so you can't actually do put call parity without making assumptions. Additionally, you often don't see the same forward implied at all strikes. $\endgroup$ – will Oct 27 '19 at 8:54
  • $\begingroup$ For European options, would the mid prices not work to use PCP and imply the Forward, and subsequently imply the vols? I can see that it is a problem for American options. Any literature on the matter? $\endgroup$ – Ramesh Kadambi Oct 27 '19 at 15:21
  • $\begingroup$ Why do you assume that the mid of the bid and the ask is the true value? If you look at prices of all the options in the chain you'll see the bid/offer is not a consistent width, and you're not going to have a smooth mid price either necessarily. $\endgroup$ – will Oct 27 '19 at 17:23

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