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Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers :

  • By Implication
  • Let's be Rational

on its website -- as well as a normal vol implying study/method (see the paper "Implied Normal Volatility").

They all concern european options, and the "by implication/let's be rational" method, even if it is simply based on the profile of the function to invert, is regarded as the quickest/most precise among practioners, especially among people constructing implied vol surfaces.

My question is : is there an analogue for the implied volatility of american options ? What's the best method (precision+speed) to do this ? (The context is the construction of implied vol surfaces.)

There is a choice of numerical method to compute the price (MC, trees, whatever) + type of solver of back out the implied vol. As the faster the solver the better I'd go for a Brent for it, which would leave only the choice of the quickest way to price the american numerically.

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    $\begingroup$ The best in terms of accuracy and speed would probably be brent with the option priced out a discrete scheme (finite difference or binomial or trinomial tree). But the resulting volatility surface (it that is what you are interested in) would be useless for computing anything other than vanilla american options. For that it would be better to calibrate a european vanilla option implied vol surface and use the corresponding Dupire local volatility surface to price any type of payoff. $\endgroup$
    – Antoine Conze
    Jun 11, 2019 at 15:36
  • $\begingroup$ What I see people doing is "Europeanize" the American option prices and then take the Implied Vol. $\endgroup$
    – Alex C
    Jun 11, 2019 at 15:44
  • $\begingroup$ @AlexC what do you mean by "europeanizing an american option" ? $\endgroup$
    – Olórin
    Jun 11, 2019 at 15:49
  • $\begingroup$ @AntoineConze In order to calibrate a european vanilla option implied vol surface and use the corresponding Dupire local volatility surface to price any type of payoff, I should have quotes of european options, but I am told that there are underlyings (equities or equity indexes) for which there's no european option market, only american. I can't find an exemple and find it hard to believe. $\endgroup$
    – Olórin
    Jun 20, 2019 at 12:35
  • $\begingroup$ @AntoineConze Simple, in fact : apple. No european market in bb datalicence. $\endgroup$
    – Olórin
    Jun 20, 2019 at 12:43

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