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## EXTENSIONS

### First extension: Multi-factor model

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The one-factor model that we used is widely used in practice and seems adequate for many portfolios. In some situations, however, dependence may be richer than what can be described through a one-factor model. In an international portfolio, for example, it may be necessary to allow within-country correlations to be larger than across-country correlations.

In a model with *K* factors, the asset value of obligor *i* is modeled as

In addition to the assumptions that we made above (see Equation (7.2)), we also assume the factors *Z _{k}* to be independent.

To implement such a model, we first need to specify as many factor sensitivities as there are factors. In Table 7.2, we could record them to the right of column E.