Volatility Smile
A common graphical shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date.
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Volatility Smile - A graphical characteristic of the implied volatility of options of the same underlying asset across different strikes forming the concave shape of a smile. Read More About Volatiliy Smile.
Any volatility smile model which prices vanilla options can therefore be used to price the variance swap. For example, using the Heston model, a closed-form solution can be derived for the fair variance swap rate.
7.1 The volatility smile
7.2 Valuing bond options
7.3 Interest rate curve
7.4 Short stock rate ...
The phenomenon of the implied volatility smile shows that the Black-Scholes (1973) formula tends to systematically misprice out-of-the-money and in-themoney options if the volatility implied from the at-the-money option is used.
By computing the volatility for all strikes on a particular underlying we obtain the volatility smile. The implied volatility is typically significantly higher for in-the-money stock and interest-rate call options, i.e.
This results in something referred to as the "volatility smile". Black Scholes can be used in reverse to calculate the implied volatility (IV) necessary to generate a given price; ...
Application: Zeta is a measure of the importance of using the volatility smile, rather than only the ATM volatility.
Source: Howard Savery, "Quantifying Volatility Convexity," Derivatives Strategy, 2/2000, pp. 54-55. Back to Top
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 See also: Stock, Option, Implied, Volatility, Market
  
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