Sticky Volatility Conventions for Equity Options

Summary

The document considers whether an equity option’s implied volatility should be adjusted when the underlying price moves. It describes alternative ways to hold the volatility surface fixed: sticky strike keeps implied volatility tied to each strike, while sticky moneyness or sticky delta ties it to the option’s relative position. Under these different conventions, a move in the underlying can imply different volatility changes, so delta alone may not capture the full price response.

The discussion connects the question to the negative relationship often observed between broad equity returns and volatility indexes, but does not establish that this relationship determines an individual option’s volatility adjustment. It notes that market behavior can vary over time and that blended or other surface dynamics are possible. The short exchange offers a conceptual distinction rather than a calibrated rule or empirical test for selecting a convention.

Key ideas

• Implied volatility may change when the underlying moves, depending on how the volatility surface is modeled.
• Sticky strike holds volatility fixed at a given strike, while sticky moneyness and sticky delta use relative option position.
• A volatility convention changes the expected vega contribution to an option-price move alongside delta.
• Observed equity and volatility-index relationships do not by themselves prescribe a universal surface-shift rule.

Tags

# For equity options, does the implied vol change if the price of the underlying does?


# For equity options, does the implied vol change if the price of the underlying does?












For example, consider S&P options.

My reasoning is rooted in the fact that VIX returns and S&P returns have a negative relationship, since VIX is a measure of S&P options' implied vol. Doesn't that imply that when the S&P goes down, the implied vol of S&P options is going up? So if you were to answer "what happens to the price of this option when the underlying increases 1%"... instead of just using the delta of the option, would it be intuitively more correct to then make an expected vega adjustment? If I a mistaken about something, please let me know.

Thanks!

## Answer by Bram (score 2)

https://quant.stackexchange.com/a/42738

Sometimes.

Two extreme models are assuming: a) ATM vol stays constant for a given moneyness (called sticky moneyness) or b) vol stays constant at fixed strikes (called sticky moneyness). A variation on a) is sticky delta. It's also possible to come up with models that are sort of a weighted average of these two extremes.

As Quantuple pointed out, work has been done by Derman to identify what the market is using; the answer is that it depends/varies over time. Googling on his name plus the terms above will get you a long way in finding more resources.

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