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Singular perturbation methods in credit derivative modeling
Descriptive
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Text
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Title
Singular perturbation methods in credit derivative modeling
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ETD_2352
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052121
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eng
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theses
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Topic
Mathematics
Subject
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Topic
Credit derivatives--Mathematical models
Subject
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(authority = ETD-LCSH)
Topic
Stochastic processes
Abstract
This thesis introduces the dynamical pricing model and
approximation method in pricing a "Collateralized Debt
Obligation" (CDO). For this purpose we use a two-dimensional, self-affecting Markov process of discrete-valued aggregate loss process and stochastic factor process in its intensity. We review several models for pricing of multi-name credit derivative
products and explain in detail a two-dimensional Markov intensity model proposed by Halperin and Arnsdorf.
Using the model by Halperin and Arnsdorf, we derive the Kolmogorov forward partial differential equation for the transition density function of the underlying two-dimensional Markov process. We use the singular perturbation method to obtain an approximate solution
to this partial differential equation in the case of a fast mean reverting stochastic intensity model. We perform an error analysis to determine the accuracy of our approximate solution.
approximation method in pricing a "Collateralized Debt
Obligation" (CDO). For this purpose we use a two-dimensional, self-affecting Markov process of discrete-valued aggregate loss process and stochastic factor process in its intensity. We review several models for pricing of multi-name credit derivative
products and explain in detail a two-dimensional Markov intensity model proposed by Halperin and Arnsdorf.
Using the model by Halperin and Arnsdorf, we derive the Kolmogorov forward partial differential equation for the transition density function of the underlying two-dimensional Markov process. We use the singular perturbation method to obtain an approximate solution
to this partial differential equation in the case of a fast mean reverting stochastic intensity model. We perform an error analysis to determine the accuracy of our approximate solution.
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electronic resource
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vi, 80 p.
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Ph.D.
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Includes bibliographical references (p. 78-79)
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by Jawon Koo
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Koo
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Jawon
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1976-
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Jawon Koo
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Feehan
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Paul
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chair
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Paul M.N. Feehan
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Ocone
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Daniel
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internal member
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Daniel Ocone
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Gundy
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Richard
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Richard Gundy
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Chen
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Ren-Raw
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Ren-Raw Chen
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Rutgers University
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Graduate School - New Brunswick
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2010
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2010-01
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xx
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Rutgers University Electronic Theses and Dissertations
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ETD
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
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doi:10.7282/T3FQ9WRD
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Copyright protected
Notice
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Availability
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Open
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Permission or license
Note
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Koo
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Jawon
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2010-01-02 23:17:47
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Jawon Koo
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Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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