Option Pricing with Generalized Logistic Distributions(published in:Global Economic Review, (2014) Vol.43, NO.3)

We start from deriving several option pricing formulas of which the prices of underlying asset follow three different commonly used heavy-tailed distribution functions; Generalized Pareto Distribution, Generalized Logistic Distribution, and Generalized Extreme Value Distribution. The derived option pricing formulas differently characterize the probabilities of extreme events in financial markets, so that these can be used to overcome the conventional ¡°normal¡± market assumption by capturing the negative skewness and/or excess kurtosis of financial asset returns. We then compare how option prices behave depending on the assumed distributions with their scale and shape parameters.