Option Pricing on stocks with

1
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
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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
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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