Shannon's information theory and its applications in derivative pricing

Abstract

During the past two decades Levy processes became very popular in Financial Mathematics. Truncated Levy distributions were used for model-ing by Mantegna and Stanley [13], [14]. Later Novikov [16] and Koponen [10] introduced a family of infinitely divisible analogs of these distributions. These models have been generalized by Boyarchenko and Levendorskii [5], and are known now as KoBoL models. Such models provide a good fit in many situ-ations. The main aim of this article is to shed a fresh light onto the pricing theory using regular Levy processes of exponential type. We introduce a class of payoff functions which is adopted to the set of regular Levy processes of exponential type which is important in various applications. In particular, this class includes payoff function which corresponds to the European call option. We analyze pricing formula, construct and discuss several methods of approx-imation which are almost optimal in the sense of respective n-widths. This approach has its roots in Shannon's Information Theory. © 2013 Academic Publications, Ltd.