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Parameter Estimation of the Pareto-Beta Jump-Diffusion Model in Times of Catastrophe Crisis
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Applied Mathematics and Physics (CAMP). (Financial Mathematics)
2011 (English)Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Jump diffusion models are being used more and more often in financial applications. Consisting of a Brownian motion (with drift) and a jump component, such models have a number of parameters that have to be set at some level. Maximum Likelihood Estimation (MLE) turns out to be suitable for this task, however it is computationally demanding. For a complicated likelihood function it is seldom possible to find derivatives. The global maximum of a likelihood function defined for a jump diffusion model can however, be obtained by numerical methods. I chose to use the Bound Optimization BY Quadratic Approximation (BOBYQA) method which happened to be effective in this case. However, results of Maximum Likelihood Estimation (MLE) proved to be hard to interpret.

Place, publisher, year, edition, pages
2011. , 68 p.
Keyword [en]
Financial Mathematics, Calibration, Parameter Estimation, MLE, Likelihood, BOBYQA, Jump-diffusion, Pareto-Beta
National Category
Computational Mathematics Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hh:diva-16027Local ID: IDE1125OAI: oai:DiVA.org:hh-16027DiVA: diva2:437550
Subject / course
Financial Mathematics
Presentation
2011-05-30, 11:46 (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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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