Dependent Sectors and an Extension to Incorporate Market Risk

In standard CreditRisk+ the risk factors are assumed to be independently gamma distributed and as a consequence the model can be computed analytically. If one extends the model such that the risk factors are dependently distributed with quite arbitrary distributions, one has to give up the existence of a closed-form solution. The advantage of this approach is that one gains interesting generalizations and the computational effort to determine the loss distribution still remains quite small.In the first step the model will be generalized such that the risk factors are dependently distributed with quite arbitrary distributions and as a suitable choice in practice, the dependent lognormal distribution is suggested. This model can then be transferred to a time continuous model and the risk factors become processes, more precisely geometric Brownian motions. Having a time continuous credit risk model is an important step to combining this model with market risk. Additionally a portfolio model will be presented where the changes of the spreads are driven by the risk factors. Using a linear expansion of the market risk, the distribution of this portfolio can be determined. In the special case that there is no credit risk, this model yields the well-known delta normal approach for market risk, hence a link between credit risk and market risk has been established.