Option Pricing and Distribution Characteristics

A number of flexible distributions (generalized beta of the second kind, inverse hyperbolic sine (IHS), $$g$$ g -and- $$h$$ h , Weibull, Burr-3, Burr-12, generalized gamma, reciprocal gamma) are examined in the setting of option-pricing to explore potential improvements over the standard assumption of lognormal returns. Price formulas are presented specific to each assumed distributional form. The IHS option price formula has not previously been presented in the literature. An empirical application follows where implied risk-neutral density functions for each distribution are estimated from options on the S&P 500 Index. The distributions’ performance relative to one another is then evaluated with the more flexible distributions performing similarly and outperforming their special and limiting cases, including the Black-Scholes which is based on the lognormal. Copyright Springer Science+Business Media New York 2015