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

Ahmad, Zubair (2016). Using semi-infinite optimisation to calculate price bounds for basket options. University of Birmingham. Ph.D.

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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:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):