surface, we can see that the underlying symbol has both volatility skew (a tilt along the delta axis), as well as a volatility term structure indicating an anticipated event in the near future. 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). Modeling volatility Methods of modelling the volatility smile include stochastic volatility models and local volatility models. For a discussion as to the various alternate approaches developed here, see and . See also Volatility (finance) Stochastic volatility SABR volatility model Vanna Volga method Heston model Implied binomial tree Implied trinomial tree Edgeworth binomial tree References External links Emanuel Derman, The Volatility Smile and Its Implied Tree (RISK, 7-2 February 1994, pp. 139–145, pp. 32–39) (PDF) Mark Rubinstein, Implied Binomial Trees (PDF) Damiano Brigo, Fabio Mercurio, Francesco Rapisarda and Giulio Sartorelli, Volatility Smile Modeling with Mixture Stochastic Differential Equations (PDF) Visualization of the volatility smile C. Grunspan, "Asymptotics Expansions for the Implied Lognormal Volatility : a Model Free Approach" Y. Li, "A mean bound financial model and options pricing" examples of commodity volatility smiles/skews Mathematical finance Options (finance)