The fair value of an option is given by breakeven volatility, the value of implied volatility that sets the profit and loss of a delta-hedged option to zero. We calculate breakeven volatility for 400,000 options traded on the S&P 500 Index, and we build a predictive model for these volatility...

The common practice of using different volatilities for options of different strikes in the Black-Scholes (1973) model imposes inconsistent assumptions on underlying securities. The phenomenon is referred to as the volatility smile. This paper addresses this problem by replacing the Brownian...