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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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  • Thesis.pdf
    • Introduction
    • I Density Approach for Credit Derivatives' Modeling
      • Enlargement of Filtrations
        • Introduction
        • Framework and preliminaries
        • Some measurability properties
        • Expectation and projection tools
        • Martingales' characterization
        • Canonical decomposition
          • General results
          • Results under E-hypothesis
          • Comparing with Yor's results
        • Predictable representation theorems
        • Girsanov's theorem
        • Some statements about H-hypothesis
        • Multidimensional case
        • Conclusion
      • Construction of Density Models
        • Introduction and Preliminaries
        • Conditional law of a random variable
          • A Gaussian example
          • A Gamma example
        • Change of probability
        • Cox construction and generalization
          • Canonical Cox construction
          • Generalized Cox construction
        • Convexity construction
        • Filtering-based examples
        • Starting from a survival process
        • Multidimensional models
        • Conclusion
      • Hedging Credit Derivatives in the Density Approach
        • Introduction
        • Hedging defaultable zero coupon bonds
        • Hedging a CDO tranche with CDSs
          • Model
          • Decomposition of H-martingales
          • Dynamics of price processes
          • Hedging Portfolio
        • General case
        • Conclusion
    • II Counterparty Risk on a CDS
      • A Markov Chain Model with Joint Defaults
        • Introduction
          • Counterparty Credit Risk
          • A Markov Copula Approach
        • General Set-Up
          • Cash Flows
          • Pricing
          • Special Case G=H
        • Markov Copula Factor Set-Up
          • Factor Process Model
          • Pricing
          • Hedging
        • Implementation
          • Affine Intensities Model Specification
          • Numerical Results
        • Concluding Remarks and Perspectives
      • Valuation and Hedging of Counterparty Exposure: the Impact of Stochastic Spreads
        • Introduction
        • Cash Flows and Pricing in a General Set-Up
        • Model
        • Pricing
        • Hedging of Counterparty Exposure
          • Dynamics of Cumulative CVA
          • Hedging of CVA
        • Model Implementation
          • Marginals
          • Joint Defaults
          • Calibration
        • A Variant of the Model with Extended CIR Intensities
          • Implementation
        • Numerical Results
          • Calibration to Market Data
          • CVA Stylized Features
          • Case of a Low-Risk Reference Entity
          • Spread Options Implied Volatilities
        • Conclusions
      • Proof of Proposition 4.3
      • Generalized CIR processes
      • Bibliography
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