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Mathematical Preliminaries

In: Pricing and Risk Management of Synthetic CDOs

Author

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  • Anna Schlösser

    (Hedging and Derivatives Strategies)

Abstract

In this chapter the mathematical preliminaries relevant for this thesis are provided. First of all, we present the basic definitions and the central facts of the stochastic calculus. In the second section, one of the most popular reduced-form single-name credit risk models, namely the default intensity model is described. This model is going to be used in the further chapters for CDS and CDO modeling. We will not discuss the variety of the single-name credit risk models in this thesis, since we concentrate on the portfolio credit risk and correlation modeling. In the third section, the central facts and estimation algorithms of the Hidden Markov Models theory are covered. Finally, the structure of the rating migration matrices and computation of the migration probabilities is discussed in the fourth section.

Suggested Citation

  • Anna Schlösser, 2011. "Mathematical Preliminaries," Lecture Notes in Economics and Mathematical Systems, in: Pricing and Risk Management of Synthetic CDOs, chapter 0, pages 67-92, Springer.
  • Handle: RePEc:spr:lnechp:978-3-642-15609-0_3
    DOI: 10.1007/978-3-642-15609-0_3
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