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Essays on Esscher Pricing Measures and Densities

  • Author / Creator
    Alsemary, Haya
  • This thesis investigates the important statistical tool of Esscher transform with its applications in mathematical finance for various environments. This transformation was introduced by F. Esscher and it became very popular afterwards, in both actuarial sciences and finance due to its role in premium calculations and pricing. The thesis discusses the Esscher pricing measure (or equivalently density) for both the discrete and continuous time settings. In discrete time, we describe the Esscher martingale measure for the general case, and we illustrate the results on the two popular models for stock, namely the binomial and trinomial models. In the continuous time framework, we focus on the Black-Scholes model for stock (geometric Brownian motion) only. The innovation of this thesis lies principally in considering two level of informations: The ``public" flow information denoted by $\mathbb F$ that represents the flow of information available to all agents through time, and a bigger flow of information denoted by $\mathbb G$. This latter flow of information incorporates both the flow $\mathbb F$ and the information about a death time of an agent $\tau$ as it occurs. Thus, for this larger flow of information, we describe the Esscher martingale measures, and the Esscher prices for death-linked contracts. The Greeks of these Esscher prices are derived as well, besides the comparison with the Black-Scholes pricing formula

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R37W67N53
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.