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I have implied volatility data for call and put options (expiring in 1 month from any given date) for a particular stock. In addition, I have the delta for the options.

However, I have no information about the spot price of the stock or the strike price of the options.

How do I draw a volatility smile from the given data?

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First off, volatility smiles are often drawn over a delta space.

Since you're asking, I'll assume you're trying to draw a volatility smile over strike prices, log moneyness, or some similar metric. If you have neither the spot price nor any strike prices associated with your data, I don't believe it's possible to back out both of those values. Not absolutely certain, but I assume there must be infinite possibilities. If you just had the spot price, you could back out all the strikes with ease.

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  • $\begingroup$ The spot price is publicly available on yahoo/google finance or even the company website. One can back out the strikes and then plot the smile using strikes on X-axis and implied vol on Y-axis. $\endgroup$
    – Eli
    Aug 27, 2014 at 22:06
  • $\begingroup$ OP explicitly stated he does not have the spot price. You can't even be sure he's talking about equity data. $\endgroup$
    – ch-pub
    Aug 27, 2014 at 22:08
  • $\begingroup$ However, given delta and associated volatilities, it is possible to convert those strikes to percentages of the forward $\endgroup$
    – Bram
    Aug 28, 2014 at 1:28
  • $\begingroup$ @Bram yes, I agree. $\endgroup$
    – ch-pub
    Aug 28, 2014 at 2:09
  • $\begingroup$ @nsw, I believe "options on a particular stock" indicates that the context is equity options. $\endgroup$
    – Eli
    Oct 8, 2014 at 18:04

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