Topic summary
Volatility surface
Extracted from the Wikipedia article Volatility smile.
Implied volatility surface
It is often useful to plot implied volatility as a function of both strike price and time to maturity. The result is a two-dimensional curved surface plotted in three dimensions whereby the current market implied volatility (z-axis) for all options on the underlying is plotted against the strike price (y-axis) and time to maturity (x-axis "DTM"). This defines the absolute implied volatility surface; changing coordinates so that the strike price is replaced by delta yields the relative implied volatility surface.