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Credit Risk and Credit Derivatives :Mathematical Modeling and Numerical Simulation

Zargari, Behnaz | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: English
  3. Document No: 46578 (02)
  4. University: Sharif University of Technology; Universite d'Evry Val d'Essonne
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohuri Zangeneh, Bijan; Jeanblanc, Monique; Zamani, Shiva; Crépey, Stéphane
  7. Abstract:
  8. This thesis deals with credit derivatives modeling and consists of two parts:The first part concerns the density model, recently proposed by El Karoui et al. [46], where the standing assumption is that the conditional law of default time given the reference filtration is equivalent to its (non-conditional) law. Under this assumption, we provide alternative (and simpler) proofs for some existing results in the theory of initial and progressive enlargement of filtrations. Also, we present some new results such as the predictable representation theorem for progressively enlarged filtration in the multidimensional case. We then propose several methods to construct density models, in both one-dimensional and multidimensional cases. Finally, we show that the density model is an efficient approach for dynamic hedging of multi-name credit derivatives.
    In the second part, a Markov model is constructed for studying the counterparty risk in a CDS contract. The wrong-way risk in this model is accounted for by the possibility of the simultaneous default of the reference name and of the counterparty. We start by considering a Markov chain model of two reference credits, the rm underlying the CDS
    and the protection seller in the CDS. In this set-up, we have semi-explicit formulae for most quantities of interest with regard to CDS counterparty risk like price, CVA, EPE or hedging strategies. We then generalize this framework to account for the spread risk by introducing stochastic factors, so that, we deal with a Markov copula model with stochastic intensities.We also address the issue of dynamically hedging the CVA with a CDS written on the counterparty. For model implementation, we consider three dierent a
  9. Keywords:
  10. Credit Derivatives ; Filtration Enlargement ; Density Based Method ; Numerical Simulation ; Mathematical Modeling ; Counterparty Risk ; Markov Copula Model

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