Is the Black-Scholes formula the only way "implied volatility" is calculated/defined in markets?
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3$\begingroup$ By de facto convention when people say "implied volatility" they mean "implied volatility according to Black Scholes". You can assume so whenever you hear "implied volatility". $\endgroup$– nbbo2Commented Mar 1, 2020 at 10:02
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$\begingroup$ @noob2 how do you think about the fact that the number that VIX has, should represent the yearly change the stocks might experience with some probability. But still the options are 30 day options? $\endgroup$– user123124Commented Mar 1, 2020 at 12:56
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$\begingroup$ By convention, volatilities are always just quoted in annualised (root-time) terms, irrespective of the actual period to which they refer. IE 30 days with VIX, but the same is true for eg 3 month FX vols. $\endgroup$– demullyCommented Mar 1, 2020 at 13:49
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3$\begingroup$ in the context of interest-rate derivatives (e.g caps) implied volatility can also refer to the normal model rather than the log-normal model. $\endgroup$– CetttCommented Mar 1, 2020 at 19:56
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1 Answer
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Unless otherwise stated, when people talk about implied volatility, they indeed mean the implied volatility under the Black-Scholes-Merton (BSM) model. In practice, it is quoted on a yearly basis and it's the information you would get from data sources such as RiskMetrics. It is also what people mean when they talk about estimating model parameters by (quasi) maximum likelihood using option prices: they are fitting the BSM-implied volatility surface.
I am not an expert on this, but I do recall an exception burried in the asset pricing literature. A very famous paper by Bakshi, Cao and Chen (1997) diagnose the capacity of models to improve on the BSM model by seeing if the volatilities they imply across moneyness and maturities is flatter (since you have just the one underlying, at some point in time, you have just the one volatility). It's an awkward way to put the problem which is probably why later papers that I have read seem to focus on matching the BSM smirk and not on finding a way to get a flatter one.
In other words, it's very unusual to run into other model implied volatilities -- at least as far as equity options are concerned.
