A Queueing Network Approach to Portfolio Credit Risk

by Mark Davis of the Imperial College, London, and
Juan C. Esparragoza of the Imperial College, London

October 31, 2004

Introduction: In the modelling of credit risk it has been always important to consider a portfolio as a whole. Moreover, both risk management and valuation has been challenged by the development of the credit risk market with instruments based on baskets such as first to default swaps and CDOs. Modelling the credit risk of a portfolio involve:

• Credible Modelling of Interaction Effects: The literature distinguish between two main interaction effects. First, common factors that influence defaults, such as the economic cycle. Second, the contagion effect where the default of an obligor may affect the probability of default of others obligors.
• Efficient Computational Methods: Many models that are convenient for a single obligor or a few of them may be computationally expensive to use for large portfolios. For example, the use of reduced form models with copula dependence structure can be cumbersome when the number of obligors increases. Algorithms of simulation/pricing must show little sensitivity in computational terms to the number of elements.
• Ease of Calibration: Together with the computational issue, a desirable property of a model is an easy calibration. It is reflected in the existence f a methodology that allows for simplicity . A parsimony with the number of parameters must be reached. While a large number of parameters may be cumbersome and redundant, too few may prove insufficient to reflect all the market data.

In the case of large portfolios it makes sense to consider the use of large-sample approximations in order to achieve efficient computational algorithms and keep easy calibrations.

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