Abstract
In this paper, we use a multivariate affine jump process to model thedowngrade intensities for several categories of business sector in credit portfolios. Since multivariate affine jump structure enables us to consider self-exciting effects as well as mutually exciting effects, the model can explain the downgrade clusters observed in the Japanese market. Also, we propose a new credit derivative named multi-downgrade protection (MDP) as an application of our model and discuss its fair pricing.
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