IJPAM: Volume 84, No. 5 (2013)


Alexander Kushpel1, Jeremy Levesley2
Department of Mathematics
University of Leicester
Leicester, LE1 7RH, UK

Abstract. During the past two decades Lévy processes became very popular in Financial Mathematics. Truncated Lévy distributions were used for modeling 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 situations. The main aim of this article is to shed a fresh light onto the pricing theory using regular Lévy processes of exponential type. We introduce a class of payoff functions which is adopted to the set of regular Lévy 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 approximation which are almost optimal in the sense of respective n-widths. This approach has its roots in Shannon's Information Theory.

Received: January 6, 2013

AMS Subject Classification: 91G20, 30E10, 60G51, 91G60, 91G80.

Key Words and Phrases: approximation, pricing theory, Lévy-driven models, $n$-width, information theory

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DOI: 10.12732/ijpam.v84i5.13 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 5