Skewed Generalized Error Distribution of Financial Assets and Option Pricing

This article investigates the empirical distributions of log-returns of several financial assets at the daily, weekly, monthly, bimonthly, and quarterly frequencies. The results indicate that the distributions possess significant skewness and leptokurtosis. These findings are attributed to strong higher-order moment dependencies which exist mainly in daily and weekly log-returns and prevent monthly, bimonthly, and quarterly log-returns from obeying the normality lawimplied by the central limit theorem. As a consequence, price changes do not follow the geometric Brownian motion often assumed in pricing options and other derivative assets. This article formally derives a skewed version of the Generalized Error Distribution (SGED) to model the empirical distribution of log-returns of financial assets and to price their call options. Under the assumptions of risk neutrality, normality of log-returns, and absence of arbitrage opportunities the SGED option-pricing model yields as special cases several well-known models for pricing options on stocks, stock indices, currencies, and currency futures