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Using semi-infinite optimisation to calculate price bounds for basket options

Ahmad, Zubair (2016)
Ph.D. thesis, University of Birmingham.

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Abstract

The use of optimisation within financial markets is rapidly increasing. There is a growing demand for a class of new and improved methods to accurately price financial options. Semi-infinite optimisation (SIO) has become a vivid research area in mathematical optimisation during the recent two decades. This is due to the fact that there are many new theoretical advances as well as a broad variety of real-life problems where this mathematical model can be applied. This thesis considers particular applications of SIO to finding bounds on the prices of basket options.

Original results have been derived for:

• Finding a lower bound on European basket call option prices.
• Calculating a lower bound on European basket call option prices, incorporating bid-ask prices within the model.
• Analysing price bounds on various types of American basket options.
• Deriving an upper bound on the price of a discretely sampled arithmetic average Asian basket option.
• Finding an upper bound on the price of an Asian basket call option, incorporating bid-ask prices.
• Calculating an upper bound on the price of an Altiplano Mountain Range option.

The models and results obtained in this thesis can be used in financial markets by investors, investment banks and hedge funds amongst others.

Type of Work:Ph.D. thesis.
Supervisor(s):Rückmann, J. J. and Németh, S. Z. and Leppinen, D.
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:6878
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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