Volatility Smile - Evolution: Sticky

Evolution: Sticky

An implied volatility surface is static: it describes the implied volatilities at a given moment in time. How the surface changes as the spot changes is called the evolution of the implied volatility surface.

Common heuristics include:

• "sticky strike" (or "sticky-by-strike", or "stick-to-strike"): if spot changes, the implied volatility of an option with a given absolute strike does not change.
• "sticky moneyness" (aka, "sticky delta"; see moneyness for why these are equivalent terms): if spot changes, the implied volatility of an option with a given moneyness (delta) does not change.

So if spot moves from $100 to $120, sticky strike would predict that the implied volatility of a $120 strike option would be whatever it was before the move (though it has moved from being OTM to ATM), while sticky delta would predict that the implied volatility of the $120 strike option would be whatever the $100 strike option's implied volatility was before the move (as these are both ATM at the time).