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By C.Bluhm, L.Overbeck & C.Wagner

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One year from today the rating of the considered counterparty may have changed due to a change in its creditworthiness. Such a rating change is called a rating migration. , d} and pi = P[Ri → d] , where the notation R → R denotes a rating migration from rating R to rating R within one year. In this chapter we will focus on a two-state approach, essentially meaning that we restrict ourselves to a setting where d = 1, Li = Ri ∈ {0, 1}, pi = P[Li = 1]. Two-state models neglect the possibility of rating changes; only default or survival is considered.

9. in [21]. , wi,K are called the country weights of counterparty i. , m). k=K0 +1 In vector notation, (1. 20) combined with (1. 21) can be written as r = βW Ψ + ε , (1. , ΨK ) means the vector of industry and country indices. This constitutes the second level of the Global Correlation ModelTM . , K), (1. 23) n=1 where δk denotes the Ψk -specific residual. Such a decomposition is typically done by a principal components analysis (PCA) of the industry and country indices. In vector notation, (1.

That in the sequel we write vectors as column vectors. g. 9. in [21]. , wi,K are called the country weights of counterparty i. , m). k=K0 +1 In vector notation, (1. 20) combined with (1. 21) can be written as r = βW Ψ + ε , (1. , ΨK ) means the vector of industry and country indices. This constitutes the second level of the Global Correlation ModelTM . , K), (1. 23) n=1 where δk denotes the Ψk -specific residual. Such a decomposition is typically done by a principal components analysis (PCA) of the industry and country indices.

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