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Valuation of Credit Derivatives

  • In this work two main approaches for the evaluation of credit derivatives are analyzed: the copula based approach and the Markov Chain based approach. This work gives the opportunity to use the advantages and avoid disadvantages of both approaches. For example, modeling of contagion effects, i.e. modeling dependencies between counterparty defaults, is complicated under the copula approach. One remedy is to use Markov Chain, where it can be done directly. The work consists of five chapters. The first chapter of this work extends the model for the pricing of CDS contracts presented in the paper by Kraft and Steffensen (2007). In the widely used models for CDS pricing it is assumed that only borrower can default. In our model we assume that each of the counterparties involved in the contract may default. Calculated contract prices are compared with those calculated under usual assumptions. All results are summarized in the form of numerical examples and plots. In the second chapter the copula and its main properties are described. The methods of constructing copulas as well as most common copulas families and its properties are introduced. In the third chapter the method of constructing a copula for the existing Markov Chain is introduced. The cases with two and three counterparties are considered. Necessary relations between the transition intensities are derived to directly find some copula functions. The formulae for default dependencies like Spearman's rho and Kendall's tau for defined copulas are derived. Several numerical examples are presented in which the copulas are built for given Markov Chains. The fourth chapter deals with the approximation of copulas if for a given Markov Chain a copula cannot be provided explicitly. The fifth chapter concludes this thesis.
  • Bewertung von Kreditderivaten

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Metadaten
Author:Svitlana Stotska
URN (permanent link):urn:nbn:de:hbz:386-kluedo-26289
Advisor:Holger Kraft
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2011
Year of Publication:2011
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2011/04/04
Date of the Publication (Server):2011/05/04
Tag:Copula; Credit Default Swap; Markov Kette
Copula; Credit Default Swap; Markov Chain
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C40 Computational Markov chains
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B60 Trade models
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Gxx Mathematical finance / 91G20 Derivative securities
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011