Implied Volatility Depends on the Pricing Model and Contract Features

Summary

The document asks whether implied volatility has a strict, model-independent definition or is instead obtained by inverting a chosen option-pricing model. It focuses on equity and index options, contrasting European options on a dividend-paying index with American options on a dividend-paying stock. The motivating convention is to calibrate the Black–Scholes model to an observed market price and solve for volatility.

The examples expose a key modeling issue: contract exercise style and dividends affect the pricing assumptions used in the inversion. The text itself provides no answer, calculation, or market evidence, and does not specify a model for American exercise or dividend treatment. It is therefore best read as a conceptual question about how to interpret quoted implied volatility, not as a complete procedure for calculating it across these contracts.

Key ideas

• Implied volatility is framed as the volatility that makes a chosen pricing model match an observed option price.
• The document compares European index options and American single-stock options with dividend-paying underlyings.
• Exercise style and dividend assumptions matter when choosing a model for inversion.
• No definitive calculation method or model-specific answer is supplied.

Tags

# Is implied volatility model specific in the context of options on stocks and indices?


# Is implied volatility model specific in the context of options on stocks and indices?












I just wanted to clarify a few things around implied volatility which I've read in the Hull/Natenberg books, which I find quite confusing.

Both books refer to implied volatility in the context of a European option on a non-dividend paying underlying, and they calibrate the BS 1973 model to observed option prices and back solve for the volatility, which then gives the "implied volatility".

My question is whether this is the strict definition of implied volatility? i.e. is the "implied volatility" always the volatility calculated from observed prices using the basic BS 1973 model, at least in the context of stock indices and individual stocks?

Eg1: if I wanted to calculate the implied volatility on the S&P500 index (which are European options on a dividend paying underlying) at a certain strike and maturity - is it just a matter of calibrating the BS 1973 model to observed prices and back solving for the volatility?

Eg2: if I wanted to calculate the implied volatility on Microsoft (an American option on a dividend paying underlying) at a particular strike and maturity, would I just repeat the process in Eg1?

Any clarity on this is greatly appreciated

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