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Pricing and hedging asian options using Monte Carlo and integral transform techniques
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2010
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| _version_ | 1867613931538743296 |
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| access_status_str | Open Access |
| author | Chibawara, Trust |
| author2 | Ouwehand, P. W. |
| author_browse | Chibawara, Trust Ouwehand, P. W. |
| author_facet | Ouwehand, P. W. Chibawara, Trust |
| author_sort | Chibawara, Trust |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/4292 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:59.464Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2010 |
| publishDateRange | 2010 |
| publishDateSort | 2010 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/4292 Pricing and hedging asian options using Monte Carlo and integral transform techniques Chibawara, Trust Ouwehand, P. W. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Asian option pricing Laplace transform inversion Monte Carlo methods Dissertations -- Mathematics Theses -- Mathematics Integral transform methods Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. ENGLISH ABSTRACT: In this thesis, we discuss and apply the Monte Carlo and integral transform methods in pricing options. These methods have proved to be very e ective in the valuation of options especially when acceleration techniques are introduced. By rst pricing European call options we have motivated the use of these methods in pricing arithmetic Asian options which have proved to be di cult to price and hedge under the BlackScholes framework. The arithmetic average of the prices in this framework, is a sum of correlated lognormal distributions whose distribution does not admit a simple analytic expression. However, many approaches have been reported in the academic literature for pricing these options. We provide a hedging strategy by manipulating the results by Geman and Yor [42] for continuous xed strike arithmetic Asian call options. We then derive a double Laplace transform formula for pricing continuous Asian call options following the approach by Fu et al. [39]. By applying the multi-Laguerre and iterated Talbot inversion techniques for Laplace transforms to the resulting pricing formula we obtain the option prices. Finally, we discuss the shortcomings of using the Laplace transform in pricing options. AFRIKAANSE OPSOMMING: In hierdie tesis bespreek ons Monte Carlo- en integraaltransform metodes om die pryse van nansi ele opsies te bepaal. Hierdie metodes is baie e ektief, veral wanneer versnellingsmetodes ingevoer word. Ons bepaal eers die pryse van Europese opsies as motivering, voordat ons die bostaande metodes gebruik vir prysbepaling van Asiatiese opsies met rekenkundige gemiddeldes, wat baie moeiliker is om te hanteer in die BlackScholes raamwerk. Die rekenkundige gemiddelde van batepryse in hierdie raamwerk is 'n som van gekorreleerde lognormale distribusies wie se distribusie nie oor 'n eenvoudige analitiese vorm beskik nie. Daar is egter talle benaderings vir die prysbepaling van hierdie opsies in die akademiese literatuur. Ons bied 'n verskansingsstrategie vir Asiatiese opsies in kontinue tyd met 'n vaste trefprys aan deur die resultate van Geman en Yor [42] te manipuleer. Daarna volg ons Fu et al. [39] om 'n dubbele Laplace transform formule vir die pryse af te lei. Deur toepassing van multi-Laguerre en herhaalde Talbotinversie tegnieke vir Laplace transforms op hierdie formule, bepaal ons dan die opsiepryse. Ons sluit af met 'n bespreking van die tekortkominge van die gebruik van die Laplace transform vir prysbepaling. 2010-02-25T05:32:26Z 2010-08-13T15:01:09Z 2010-02-25T05:32:26Z 2010-08-13T15:01:09Z 2010-03 Thesis http://hdl.handle.net/10019.1/4292 en University of Stellenbosch 90 p. application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Asian option pricing Laplace transform inversion Monte Carlo methods Dissertations -- Mathematics Theses -- Mathematics Integral transform methods Chibawara, Trust Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title | Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title_full | Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title_fullStr | Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title_full_unstemmed | Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title_short | Pricing and hedging asian options using Monte Carlo and integral transform techniques |
| title_sort | pricing and hedging asian options using monte carlo and integral transform techniques |
| topic | Asian option pricing Laplace transform inversion Monte Carlo methods Dissertations -- Mathematics Theses -- Mathematics Integral transform methods |
| url | http://hdl.handle.net/10019.1/4292 |
| work_keys_str_mv | AT chibawaratrust pricingandhedgingasianoptionsusingmontecarloandintegraltransformtechniques |