Explaining The Volatility Smile: Reduced-Form Vs. Structural Option Models

The authors employ a "Reduced-form" approach to price European options. In contrast to "Structural" models that assume stochastic processes for the underlying state variable(s), "Reduced-form" models such as Stutzer (1996), Eberlein, Keller and Prause (1998), and Cochrane and Saa-Requejo (2000), directly fit the end distribution of the underlying state variable(s) with flexible statistical distributions. They derive an approximation formula that prices S&P 500 index options in closed form. Their model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models.