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Applications in Mathematical Finance

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Queues and Lévy Fluctuation Theory

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Abstract

This chapter covers financial applications. First a brief survey is given on the specific Lévy processes that are frequently used to model financial processes (such as the evolution of an asset price); special attention is paid to the normal inverse Gaussian process, the variance gamma process, and the generalized tempered stable process (which also covers the CGMY process). Then we explain how Lévy processes can be estimated from data. A substantial part of this chapter focuses on the computation of prices of exotic options, such as the barrier option and the lookback option, whose payoff functions can be expressed in terms of the extreme values (over a given time horizon) that are attained by the price of the underlying asset. The chapter is concluded by an account of the use of Lévy fluctuation theory in non-life insurance.

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Authors and Affiliations

  1. Mathematical Institute, University of Wrocław, Wrocław, Poland

    Krzysztof Dębicki

  2. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    Michel Mandjes

Authors
  1. Krzysztof Dębicki
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  2. Michel Mandjes
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Dębicki, K., Mandjes, M. (2015). Applications in Mathematical Finance. In: Queues and Lévy Fluctuation Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-20693-6_15

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