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Stochastic Processes in Credit Risk Modelling

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  • Roberto Casarin

Abstract

In credit risk modelling, jump processes are widely used to de- scribe both default and rating migration events. This work is mainly a review of some basic de nitions and properties of the jump processes intended for a preliminary step before more ad- vanced lectures on credit risk modelling. We focus on the Poisson process and some generalisations, like the compounded and the double stochastic Poisson processes, which are widely used for describing the time-inhomogeneous dynamic either of the default process or of the credit rating transition. As such, much of the material is not new, but focused and organized from a credit risk perspective. Moreover it contains detailed proofs of some funda- mental results. Other original contributions come from examples and simulated studies, which help the reader to better understand the features of the described processes.

Suggested Citation

  • Roberto Casarin, 2005. "Stochastic Processes in Credit Risk Modelling," Working Papers ubs0505, University of Brescia, Department of Economics.
    • Handle: RePEc:ubs:wpaper:ubs0505
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    References listed on IDEAS

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    1. Serge Darolles & Christian Gourieroux & Joanna Jasiak, 2001. "Compound Autoregressive Models," Working Papers 2001-21, Center for Research in Economics and Statistics.
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    3. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    4. Schönbucher, Philipp J., 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers 15/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
    5. Pierre Druilhet, 2001. "Conditions for Optimality in Experimental Designs," Working Papers 2001-20, Center for Research in Economics and Statistics.
    6. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    7. Christian Gourieroux & Alain Monfort, 2002. "Equidependence in Qualitative and Duration Models with Application to Credit Risk," Working Papers 2002-51, Center for Research in Economics and Statistics.
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