Black-Scholes Implied Volatility as the Market Convention

Summary

The document explains that, unless a different model is specified, market references to implied volatility generally mean the volatility obtained by inverting the Black-Scholes-Merton option pricing formula. It describes this measure as commonly quoted on an annual basis and used when fitting model parameters to option prices. In that setting, researchers often work with a surface of Black-Scholes implied volatilities across strikes and maturities.

The discussion mentions an asset-pricing research exception: some studies compare alternative models by asking whether their implied volatilities are flatter across moneyness and maturity. The answer characterizes such alternative model-implied volatility measures as uncommon in equity options, and notes that later work often focuses on matching the observed Black-Scholes volatility smile or skew. This is a brief overview rather than a survey of conventions across all asset classes, and the author signals limited expertise on the research exception.

Key ideas

• Market usage usually means Black-Scholes-Merton implied volatility unless another model is specified.
• Implied volatility is commonly quoted annually and can be represented across strikes and maturities as a surface.
• Option prices can be used to fit model parameters through their Black-Scholes implied volatilities.
• Some research evaluates models by the shape of their implied volatility across moneyness and maturity.
• Alternative model-implied volatility conventions are described as uncommon for equity options.

Tags

# Black-Scholes formula and implied vol


# Black-Scholes formula and implied vol












Is the Black-Scholes formula the only way "implied volatility" is calculated/defined in markets?

## Answer by Stéphane (score 2, accepted)

https://quant.stackexchange.com/a/51438

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.