155
IRUS Total
Downloads
  Altmetric

On the valuation of barrier and American options in local volatility models with jumps

File Description SizeFormat 
Eriksson-B-2013-PhD-Thesis.pdfThesis1.13 MBAdobe PDFView/Open
Title: On the valuation of barrier and American options in local volatility models with jumps
Authors: Eriksson, Bjorn
Item Type: Thesis or dissertation
Abstract: In this thesis two novel approaches to pricing of barrier and American options are developed in the setting of local volatility models with jumps: the moments method and the Markov chain method. The moments method is a valuation approach for barrier options that is based on a characterisation of the exit location measure and the expected occupation measure of the price process of the underlying in terms of the corresponding moments. It is shown how the value of barrier-type derivatives can be expressed using these moments, which are in turn shown to be characterised by an infinite-dimensional linear system. By solving finite-dimensional linear programming problems, which are obtained by restricting to moments of a finite degree, upper and lower-bounds are found for the values of the options in question. The Markov chain method for the valuation of American options is based on an approximation of the underlying price process by a continuous-time Markov chain. The value-function of the American option driven by the approximating chain is identified by solving the associated optimal stopping problem. In particular, a novel explicit characterisation of the optimal exercise boundary is derived in terms of the generator of the Markov chain. Using this characterisation it is shown that the optimal exercise boundary and the corresponding value-function can be evaluated efficiently. For both of the presented methods convergence results are established. The methods are implemented for a range of local volatility models with jumps, and a number of numerical examples are discussed in detail to illustrate the scope of the methods.
Content Version: Open Access
Issue Date: Sep-2013
Date Awarded: Dec-2013
URI: http://hdl.handle.net/10044/1/28104
DOI: https://doi.org/10.25560/28104
Supervisor: Pistorius, Martijn
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/D039053
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses



Unless otherwise indicated, items in Spiral are protected by copyright and are licensed under a Creative Commons Attribution NonCommercial NoDerivatives License.

Creative Commons