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Pricing of exotic options under the Kou model by using the Laplace transform
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
2011 (English)Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis we present the Laplace transform method of option pricing and it's realization, also compare it with another methods. We consider vanilla and exotic options, but more attention we pay to the two-asset correlation options. We chose the one of the modifications of Black-Scholes model, the Kou double exponential jump-diffusion model with the double exponential distribution of jumps, as model of the underlying stock prices development. The computations was done by the Laplace transform and it's inversion by the Euler method. We will present in details proof of finding Laplace transforms of put and call two-asset correlation options, the calculations of the moment generation function of the jump-diffusion by Levy-Khintchine formulae in cases without jumps and with independent jumps, and direct calculation of the risk-neutral expectation by solving double integral. Our work also contains the programme code for two-asset correlation call and put options. We will show the realization of our programme in the real data. As a result we see how our model complies on the NASDAQ OMX Stock-holm Market, considering the two-asset correlation options on three cases by stock prices of Handelsbanken, Ericsson and index OMXS30.

Place, publisher, year, edition, pages
2011. , 73 p.
Keyword [en]
Financial Mathematics, Double exponential jump-diusion model, Kou model, Laplace transform, Laplace transform inversion, two-dimensional Euler algorithm, two-asset correlation options.
National Category
Computational Mathematics Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hh:diva-16023Local ID: IDE1122OAI: oai:DiVA.org:hh-16023DiVA: diva2:437489
Subject / course
Financial Mathematics
Presentation
2011-05-31, Wigforshallen, Halmstad University, Halmstad, 09:00 (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2011-08-30 Created: 2011-08-29 Last updated: 2011-09-06Bibliographically approved

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fulltext(1117 kB)742 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf