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Theses

Risque de crédit: modélisation et simulation numérique.

Abstract : The thesis is motivated by the problems related to the defaults correlation in the portfolio credit derivatives. The thesis contains two parts. The first one is devoted to the analysis of successive defaults. We propose a new approach, based on the density of the conditional survival probabilities, to study the phenomena after the first default by determining the compensators of successive defaults and by calculating the conditional expectations with respect to the global filtration of the market. In the second part, we present an approximation method the evaluate the CDOs, using the Stein's method and the zero bias transformation. We obtain a correction term for the normal approximation and we estimate the convergence speed. Numerical tests show the efficiency of this method compared to the classical methods. We also establish similar results for Poisson approximation by adopting a discrete version of the method. Ar last for more regular functions, we proposer high-ordered corrections.
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Submitted on : Thursday, July 29, 2010 - 10:43:07 AM
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Ying Jiao. Risque de crédit: modélisation et simulation numérique.. Optimisation et contrôle [math.OC]. Ecole Polytechnique X, 2006. Français. ⟨pastel-00002180⟩

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