In this chapter we discuss the link between the CreditRisk+ loss distribution and the moment-generating function (MGF) of the risk factors. We show that the probability-generating function (PGF) of the loss variable is the MGF of the factors, evaluated at a particular “point”. This approach has two major advantages: it leads to a new recursion formula for the portfolio loss distribution that is faster and more accurate than the standard approach. It also allows us to extend the modelling framework to a wider class of factor distributions incorporating sector correlations. At the end of this chapter we show that risk contributions are related to the partial derivatives of the MGF. We derive the formula for exact risk contributions in this generalized modelling framework and highlight the differences from the corresponding result obtained in the saddlepoint approximation.
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