Approximation of prices for average-type options via bounds

Alexander, Scott Anthony

Approximation of prices for average-type options via bounds

Alexander, Scott Anthony

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Publication Type:: Thesis
Issue Date:: 2017

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Field	Value	Language
dc.contributor.author	Alexander, Scott Anthony
dc.date.accessioned	2017-04-06T03:00:40Z
dc.date.available	2017-04-06T03:00:40Z
dc.date.issued	2017
dc.identifier.uri	http://hdl.handle.net/10453/90288
dc.description	University of Technology Sydney. Faculty of Science.	en_AU
dc.description.abstract	The problem of pricing multi-dimensional arithmetic average-type options is a complex problem both analytically and numerically, analytically because the distribution of the average on which the payoff function depends is unknown in closed-form and numerically because of the high dimensionality of the problem. In this thesis we develop methods that avoid these issues by providing price approximations in the form of lower and upper bounds. We do so by approximating the event that the option finishes in-the-money with a closely related proxy and use an optimisation procedure to tighten up the bounds. The result is a pricing tool that provides accurate approximations without suffering from the exponential curse of dimensionality associated with other techniques. The method is developed for underlying assets modelled as exponential Lévy processes and numerical examples are provided under a variety of these models.	en_AU
dc.format	Thesis (PhD)
dc.language.iso	en_AU	en_AU
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/90288/2/02Whole.pdf
dc.rights	au.edu.uts.lib/ppc
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Multi-dimensional arithmetic average-type options.	en
dc.subject	Payoff function.	en
dc.subject	Dimensionality.	en
dc.subject	Price approximations in the form of lower and upper bounds.	en
dc.subject	Optimisation procedure.	en
dc.subject	Exponential Lévy processes.	en
dc.title	Approximation of prices for average-type options via bounds	en_AU
dc.type	Thesis	en_AU
utslib.copyright.status	open_access

Abstract:

The problem of pricing multi-dimensional arithmetic average-type options is a complex problem both analytically and numerically, analytically because the distribution of the average on which the payoff function depends is unknown in closed-form and numerically because of the high dimensionality of the problem. In this thesis we develop methods that avoid these issues by providing price approximations in the form of lower and upper bounds. We do so by approximating the event that the option finishes in-the-money with a closely related proxy and use an optimisation procedure to tighten up the bounds. The result is a pricing tool that provides accurate approximations without suffering from the exponential curse of dimensionality associated with other techniques. The method is developed for underlying assets modelled as exponential Lévy processes and numerical examples are provided under a variety of these models.

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