Alternatives to the classic Black-Scholes and Merton approach to option pricing include formulae based on characteristic function of returns. Assuming independence of daily returns, this opens new ways for statistical exploration of option pricing based rather on historical data than on arbitrary choice of one of the analytically convenient classes of probability distributions like normal, Student’s t or one of the families of Levy distributions including Var-Gamma or hyperbolic. We rely on Lewis (2001) approach to pricing options based on characteristic functions of returns and show that the empirical version of this approach is a consistent estimator of the theoretical formula. In the empirical part of the project we explore the degree of agreement of this approach with the historical option prices. We show that by introducing some implied parameters one can achieve a very good agreement with the historical data. We will discuss the validity and interpretation of the model and its implied parameters.
About the speaker: Andrzej Kozek is Associate Professor at the Department of Statistics, Macquarie University. He is interested in statistical inference, in particular nonparametrics and robustness, and in applications of statistics in finance.