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?


1 Answer 1


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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.