Option Pricing on stocks with Log-Symmetric Distributions of Returns Zinoviy Landsman Fima Klebaner University of Haifa, Haifa Monash University, Melbourne Bar Ilan University 2008

In the classical, BS approach to option pricing it is assumed “a priori" that the daily returns on assets have a lognormal distribution Empirical evidence shows that log daily returns for some assets have symmetric distributions with tails different to normal We show that the classical martingale approach to option price can be applied for much general class of log symmetric distributions of returns. We give a correction to BS formula for this case

Log-symmetric distributions belong to the log-elliptical family of distributions considered by Fang et al (1990). It includes important classes of log student (log-t), log exponential power family (log EPF), log Bessel and log mixtures Now we outline the main features of the proposed model and show that just using the main properties of log symmetric class it is possible to fit this class into the framework of no-arbitrage option price theory