Editing Volatility smile (section)

==Implied volatility surface==

It is often useful to plot implied volatility as a function of both strike price and time to maturity.<ref>{{cite journal |first=Babak |last=Mahdavi Damghani |year=2013|title= De-arbitraging With a Weak Smile: Application to Skew Risk |journal=[[Wilmott (magazine)|Wilmott]] |volume=2013 |issue=1 |pages=40–49 |doi= 10.1002/wilm.10201}}</ref> 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 price (''y''-axis) and time to maturity (''x''-axis "DTM"). This defines the '''absolute implied volatility surface'''; changing coordinates so that the price is replaced by [[Greeks (finance)#Delta|delta]] yields the '''relative implied volatility surface'''.

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 put 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.

[[Image:Ivsrf.gif]]