Models for option pricing based on empirical characteristic function of returns
The standard Merton-Black-Scholes formula for European Option pricing serves only as approximation to real values of options. More advanced extensions include applications of Lévy processes and are based on characteristic functions, which are more convenient to use than the corresponding probability distributions. We found one of the Lewis (2001) general theoretical formulae for option pricing based on characteristic functions particularly suitable for a statistical approach to option pricing. By replacing the unknown theoretical characteristic function with the empirical one the obtained model can be considered as a consistent estimator of the original Lewis formula. We explore the behaviour of this model on empirical data and conclude that it is necessary to allow for two additional implied parameters to obtain option pricing superior to other models reported in the literature.