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Convergence of Option Rewards
Mälardalen University, School of Education, Culture and Communication.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and five articles devoted to optimal stopping problems of American type options. In article A, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A, B, C and E.In article B, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying assets. An approximative binomial-trinomial tree algorithm for the reselling model is constructed. In article C, we continue our study of optimal reselling of European options and give the complete solution of the approximation problem. In the article D, we consider general knockout options of American type. A Monte-Carlo method is used to study structure of optimal stopping domains generated by combinations of different pay-off functions and knockout domains.In article E the American option with knock out domains is considered. In order to show convergence of the reward functional the problem is reformulated in such a way that the convergence results in paper A can be applied.

Place, publisher, year, edition, pages
Västerås: Mälardalen University , 2010.
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 89
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-10327ISBN: 978-91-86135-84-3 (print)OAI: oai:DiVA.org:mdh-10327DiVA: diva2:352650
Public defence
2010-11-12, Kappa, Högskoleplan 1, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2010-09-22 Created: 2010-09-21 Last updated: 2010-10-21Bibliographically approved
List of papers
1. Convergence of option rewards for multivariate price processes
Open this publication in new window or tab >>Convergence of option rewards for multivariate price processes
2013 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 85, 53 p.115-131 p.Article in journal (Refereed) Published
Abstract [en]

American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes.Convergence results areobtained for optimal reward functionals of American type options forperturbed multivariate Markov processes. Theseresults are applied to approximation tree type algorithms forAmerican type options for exponential diffusion type price processes.Application to mean-reverse price processes used to model stochasticdynamics of energy prices are presented. Also application to reselling of European options are given.

Publisher
53 p.
Keyword
American option; Convergence of option rewards; binomial-trinomial tree approximation; optimal stopping; skeleton approximation; multivariate Markov price process
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-8064 (URN)10.1090/S0094-9000-2013-00879-5 (DOI)2-s2.0-84877857656 (Scopus ID)
Available from: 2010-02-11 Created: 2010-02-11 Last updated: 2015-01-30Bibliographically approved
2. Reselling of options and convergence of option rewards
Open this publication in new window or tab >>Reselling of options and convergence of option rewards
2008 (English)In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 30, no 3-4Article in journal (Refereed) Published
Abstract [en]

We consider the problem of optimal reselling of Europeanoptions. A bivariate exponential diffusion process is used todescribe the reselling model. In this way, the reselling problem isimbedded to the model of finding optimal reward for American typeoption based on this process. Convergence results are obtained foroptimal reward functionals of American type options for perturbedmulti-variate Markov processes. An approximation  bivariate treemodel is constructed and convergence of optimal expected reward forthis tree model to the optimal expected reward for the correspondingAmerican type option is proved

Keyword
European option, reselling problem, American option, reward convergence, optimal stopping, skeleton approximation, Markov process, binomial-trinomial approximation.
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-5083 (URN)
Available from: 2009-02-10 Created: 2009-02-10 Last updated: 2017-02-15Bibliographically approved
3. Optimal stopping and reselling of European options
Open this publication in new window or tab >>Optimal stopping and reselling of European options
2010 (English)In: Mathematical and Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishan, N., Nikulin, M, Boston: Birkhäuser , 2010Chapter in book (Refereed)
Abstract [en]

We consider the problem of optimal reselling of European options. A bivariate exponential diffusion process is used to describe the reselling model. In this way, the reselling problem is imbedded to the model of finding optimal reward for American type option based on this process. Convergence results are formulated for optimal reward functionals of American type options for perturbed multi-variate Markov processes. An approximation bivariate tree model is constructed and convergence of optimal expected reward for this tree model to the optimal expected reward for the corresponding reselling model is proved. 

Place, publisher, year, edition, pages
Boston: Birkhäuser, 2010
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-10283 (URN)10.1007/978-0-8176-4971-5_29 (DOI)000292954700029 ()978-0-8176-4970-8 (ISBN)
Available from: 2010-09-09 Created: 2010-09-09 Last updated: 2015-01-30Bibliographically approved
4. Simulation studies of stopping domains for American knock out options
Open this publication in new window or tab >>Simulation studies of stopping domains for American knock out options
(English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758Article in journal (Refereed) Accepted
Identifiers
urn:nbn:se:mdh:diva-10284 (URN)
Available from: 2010-09-09 Created: 2010-09-09 Last updated: 2013-02-05Bibliographically approved
5. Convergence of American knock out options in discrete time.
Open this publication in new window or tab >>Convergence of American knock out options in discrete time.
2010 (English)Report (Other academic)
Publisher
18 p.
Identifiers
urn:nbn:se:mdh:diva-10285 (URN)
Available from: 2010-09-09 Created: 2010-09-09 Last updated: 2010-09-22Bibliographically approved

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