A comprehensive view of Markov-Functional models and their application

Lapere, Michael

A comprehensive view of Markov-Functional models and their application

Master Thesis

2006

Publisher

University of Cape Town

Department

Department of Mathematics and Applied Mathematics

Faculty

Faculty of Science

Abstract

Markov-Functional models are a very powerful class of market models which calibrate and compute prices and Greeks quickly. This dissertation explains, in detail, how Markov-Functional models work as well as discussing all of the specific models developed in the literature. It contains the key points that can be found in the present literature. We explain, in detail, all of the concepts, from the theoretical framework down to the numerical implementation of the specific models. This involves explaining the framework for Markov-Functional models, describing specific models, obtaining a deeper understanding of how the model parameters affect the results, discussing the issues involved in the implementation, implementing various models and investigating the effect of numerical and market parameters on the outcome. Various concepts, not discussed in the present literature, such as considerations for selecting a discretization grid for the numerical implementation, are developed. The practical application of Markov-Functional models is considered as well as alternative fields, such as Actuarial science, where the model can be applied. In summary, this dissertation embodies a complete discussion of the current class of Markov-Functional models.

Description

Includes bibliographical references.

Keywords

Mathematical Finance

Reference:

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