Study of some functionals of standard and fractional Brownian motions with applications in quantitative finance and statistics

Ling, TG

Study of some functionals of standard and fractional Brownian motions with applications in quantitative finance and statistics

Ling, TG

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Publication Type:: Thesis
Issue Date:: 2014

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Field	Value	Language
dc.contributor.author	Ling, TG
dc.date.accessioned	2014-03-26T04:23:48Z
dc.date.available	2014-03-26T04:23:48Z
dc.date.issued	2014
dc.identifier.uri	http://hdl.handle.net/10453/24206
dc.description	University of Technology, Sydney. Faculty of Science.	en_US
dc.description.abstract	This thesis contains results on two important problems arising in quantitative finance and statistics. The first problem is about option pricing with a volume weighted average price (VWAP) as an underlying process. The VWAP is a very important quantity in finance; it appears in Australian taxation law to specify the price of share-buybacks for publicly-listed companies and it is a standard benchmark price for market participants. Pricing options on VWAP is challenging problem from a mathematical point of view because it involves two sources of randomness: the price of the asset and its traded volume. To solve the problem we have applied the moment-matching approach to a range of “stock and volume” models and as a result obtained an accurate approximation for prices of “call” options. All results have been verified by intensive Monte Carlo simulation. The second problem is concerned with study of analytical properties and simulation algorithms for a fractional Brownian motion (fBm) which is considered a good alternative to modelling stochastic processes with long range dependence in modern Mathematical finance. In particular, we have reviewed the known simulation algorithms and have implemented the fastest of them (“circulant embedding”) on a modern multicore computer. We applied the algorithm to two longstanding open problems in statistics, namely, to study distributions of exponential functionals of fBm and the maximum of fBm. The results of our simulations exhibit new and striking properties of these distributions.	en_US
dc.format	Thesis (PhD)	en_US
dc.language.iso	en	en_US
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/24206/2/02whole.pdf
dc.rights	au.edu.uts.lib/ppc
dc.rights	info:eu-repo/semantics/openAccess
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.subject	Fractional Brownian motion.	en
dc.subject	Vwap.	en
dc.subject	Volume weighted average price.	en
dc.subject	Options.	en
dc.subject	Finance.	en
dc.subject	Pricing.	en
dc.title	Study of some functionals of standard and fractional Brownian motions with applications in quantitative finance and statistics	en_US
dc.type	Thesis
utslib.copyright.status	open_access

Abstract:

This thesis contains results on two important problems arising in quantitative finance and statistics. The first problem is about option pricing with a volume weighted average price (VWAP) as an underlying process. The VWAP is a very important quantity in finance; it appears in Australian taxation law to specify the price of share-buybacks for publicly-listed companies and it is a standard benchmark price for market participants. Pricing options on VWAP is challenging problem from a mathematical point of view because it involves two sources of randomness: the price of the asset and its traded volume. To solve the problem we have applied the moment-matching approach to a range of “stock and volume” models and as a result obtained an accurate approximation for prices of “call” options. All results have been verified by intensive Monte Carlo simulation. The second problem is concerned with study of analytical properties and simulation algorithms for a fractional Brownian motion (fBm) which is considered a good alternative to modelling stochastic processes with long range dependence in modern Mathematical finance. In particular, we have reviewed the known simulation algorithms and have implemented the fastest of them (“circulant embedding”) on a modern multicore computer. We applied the algorithm to two longstanding open problems in statistics, namely, to study distributions of exponential functionals of fBm and the maximum of fBm. The results of our simulations exhibit new and striking properties of these distributions.

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http://hdl.handle.net/10453/24206