Editing Volatility smile (section)

==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. (Delta means here "Delta Volatility Adjustment", not Delta as Greek. In other words, relative volatility adjustment to ATM strike volatility which always set to be 100% moneyness as closest to the current underlying asset price and 0 for delta volatility adjustment.)

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).