A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph.

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dc.contributor.advisorBecker, Ronalden_ZA
dc.contributor.authorJoseph, Bernarden_ZA
dc.date.accessioned2014-08-13T13:22:37Z
dc.date.available2014-08-13T13:22:37Z
dc.date.issued2013en_ZA
dc.descriptionIncludes abstract.en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractWe give a review of regression-based Monte Carlo methods for pricing high-dimensional American and Bermudan options for which backwards methods such as lattice and PDE methods do not work. The continuous-time pricing problem is approximated in discrete time and the problem is formulated as an optimal stopping problem. The optimal stopping time can be expressed through continuation values (the price of the option given that the option is exercised after time j conditioned on the state process at time j). Regression-based Monte Carlo methods apply regression estimates to data generated by artificial samples of the state process in order to approximate continuation values. The resulting estimate of the option price is a lower bound. We then look at a dual formation of the optimal stopping problem which is used to generate an upper bound for the option price. The upper bound can be constructed by using any approximation to the option price. By using an approximation that arises from a lower bound method we have a general method for generating valid confidence intervals for the price of the option. In this way, the upper bound allows for a better estimate of the price to be computed and it provides a way of investigating the tightness of the lower bound by indicating whether more effort is needed to improve it.en_ZA
dc.identifier.apacitationJoseph, B. (2013). <i>A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/6076en_ZA
dc.identifier.chicagocitationJoseph, Bernard. <i>"A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013. http://hdl.handle.net/11427/6076en_ZA
dc.identifier.citationJoseph, B. 2013. A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Joseph, Bernard AB - We give a review of regression-based Monte Carlo methods for pricing high-dimensional American and Bermudan options for which backwards methods such as lattice and PDE methods do not work. The continuous-time pricing problem is approximated in discrete time and the problem is formulated as an optimal stopping problem. The optimal stopping time can be expressed through continuation values (the price of the option given that the option is exercised after time j conditioned on the state process at time j). Regression-based Monte Carlo methods apply regression estimates to data generated by artificial samples of the state process in order to approximate continuation values. The resulting estimate of the option price is a lower bound. We then look at a dual formation of the optimal stopping problem which is used to generate an upper bound for the option price. The upper bound can be constructed by using any approximation to the option price. By using an approximation that arises from a lower bound method we have a general method for generating valid confidence intervals for the price of the option. In this way, the upper bound allows for a better estimate of the price to be computed and it provides a way of investigating the tightness of the lower bound by indicating whether more effort is needed to improve it. DA - 2013 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2013 T1 - A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph TI - A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph UR - http://hdl.handle.net/11427/6076 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/6076
dc.identifier.vancouvercitationJoseph B. A survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/6076en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titleA survey of some regression-based and duality methods to value American and Bermudan options Bernard Joseph.en_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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