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Theoretical and Practical Applications of Probability: Excursions in Brownian Motion, Risk Capital Stress Testing, and Hedging of Power Derivatives
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis treats three different areas; (i) Ranked increments of stable processes and ranked excursions of Brownian motion, (ii) Sufficient capital levels for banks, and (iii) Trading strategies for reduction of the fluctuations of revenues for power plants.

The first part is a theoretcial investigation involved with the calculation of distribution functions concerning special properties of stable processes.

The second part is a description of a framework in which the sufficiency of capital levels for banks can be evaluated.

The third part is a typical example of how financial mathematics can be used to derive practical methods applicable in risk management of energy derivatives and real options.

Altogether, five papers are presented.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen , 2009. , 31 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-8570ISBN: 978-91-7155-820-6 (print)OAI: oai:DiVA.org:su-8570DiVA: diva2:200509
Public defence
2009-04-03, sal 14, hus 5, Kräftriket, Stockholm, 13:00
Opponent
Supervisors
Available from: 2009-03-12 Created: 2009-02-19Bibliographically approved
List of papers
1. Distributions of the longest excursions in a tied down simple random walk and in a Brownian bridge
Open this publication in new window or tab >>Distributions of the longest excursions in a tied down simple random walk and in a Brownian bridge
2007 In: Journal of Applied Probability, ISSN 0021-9002, Vol. 44, no 4, 1056-1067 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-25777 (URN)
Note
Part of urn:nbn:se:su:diva-8570Available from: 2009-03-12 Created: 2009-02-19Bibliographically approved
2. Ranked increments of a stable subordinator and ranked excursion lengths of Brownian motion
Open this publication in new window or tab >>Ranked increments of a stable subordinator and ranked excursion lengths of Brownian motion
Manuscript (Other academic)
Identifiers
urn:nbn:se:su:diva-25778 (URN)
Note
Part of urn:nbn:se:su:diva-8570Available from: 2009-03-12 Created: 2009-02-19 Last updated: 2010-01-13Bibliographically approved
3. Risk capital stress-testing framework and the new capital adequacy rules
Open this publication in new window or tab >>Risk capital stress-testing framework and the new capital adequacy rules
2007 In: Journal of Risk Model Validation, Vol. 1, no 3, 3-28 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-25779 (URN)
Note
Part of urn:nbn:se:su:diva-8570Available from: 2009-03-12 Created: 2009-02-19Bibliographically approved
4. Risk tolerance concepts and scenario analysis of bank capital
Open this publication in new window or tab >>Risk tolerance concepts and scenario analysis of bank capital
2009 In: Stress-testing for Financial Institutions: Applications, Regulations and Techniques, London: Risk Books , 2009, 399-422 p.Chapter in book (Other academic) Published
Place, publisher, year, edition, pages
London: Risk Books, 2009
Identifiers
urn:nbn:se:su:diva-25780 (URN)978-1-906348-11-3 (ISBN)
Note
Part of urn:nbn:se:su:diva-8570Available from: 2009-03-12 Created: 2009-02-19Bibliographically approved
5. Strips of hourly power options - Approximate hedging using average-based forward contracts
Open this publication in new window or tab >>Strips of hourly power options - Approximate hedging using average-based forward contracts
2009 (English)In: Energy Economics, ISSN 0140-9883, E-ISSN 1873-6181, Vol. 31, no 3, 348-355 p.Article in journal (Refereed) Published
Abstract [en]

We study approximate hedging strategies for a contingent claim consisting of a strip of independent hourly power options. The payoff of the contingent claim is a sum of the contributing hourly payoffs. As there is no forward market for specific hours, the fundamental problem is to find a reasonable hedge using exchange-traded forward contracts, e.g. average-based monthly contracts. The main result is a simple dynamic hedging strategy that reduces a significant part of the variance. The idea is to decompose the contingent claim into mathematically tractable components and to use empirical estimations to derive hedging deltas. Two benefits of the method are that the technique easily extends to more complex power derivatives and that only a few parameters need to be estimated. The hedging strategy based on the decomposition technique is compared with dynamic delta hedging strategies based on local minimum variance hedging, using a correlated traded asset.

Keyword
Hedging; Power option; Black76; Swing option; Local minimum variance hedging
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-25781 (URN)10.1016/j.eneco.2008.11.010 (DOI)000265478500003 ()
Note
Part of urn:nbn:se:su:diva-8570Available from: 2009-03-12 Created: 2009-02-19 Last updated: 2010-07-19Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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