Usage
• 114 views

# 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
Fall 2018
• Type of Item
Thesis
• Degree
Master of Science
• DOI
https://doi.org/10.7939/R37W67N53