Volatility Smile - Implied Volatility Surface

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 three-dimensional curved surface whereby the current market implied volatility (Z-axis) for all options on the underlying is plotted against strike price (Y-axis "Delta") and time to maturity (X-axis "DTM").

The implied volatility surface simultaneously shows both volatility smile and term structure of volatility. Option traders use an implied volatility plot to quickly determine the shape of the implied volatility surface, and to identify any areas where the slope of the plot (and therefore relative implied volatilities) seems out of line.

The graph shows an implied volatility surface for all the call options on a particular underlying stock price. The Z-axis represents implied volatility in percent, and X and Y axes represent the option delta, and the days to maturity. Note that to maintain put-call parity, a 20 delta put must have the same implied volatility as an 80 delta call. For this 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.