By C.Bluhm, L.Overbeck & C.Wagner
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Additional resources for An Introduction to Credit Risk Modeling
M ) . t. , m), (1. , ΨK are country indices. , wi,K0 are called the industry weights 17 That 18 Note is, normalized in order to have mean zero and variance one. that in the sequel we write vectors as column vectors. g. 9. in . , 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 .
1. In the context of two-state models, an approach by means of Bernoulli random variables is most natural. When it comes to ©2003 CRC Press LLC the modeling of defaults, CreditMetricsTM and the KMV-Model follow this approach. Another common approach is the modeling of defaults by Poisson random variables. 2) from Credit Suisse Financial Products is among the major industry models and a well-known representative of this approach. 3. However, in  it is shown that the models are not really compatible, because the corresponding mixture models (Bernoulli respectively Poisson variables have to be mixed in order to introduce correlations into the models) generate loss distributions with significant tail differences.
1. 6 indicate the critical thresholds or default points for each of the processes. Regarding the calibration of these default points we refer to Crosbie  for an introduction. Now let us start with the KMV-Model, which is called the Global Correlation ModelTM . Regarding references we must say that KMV itself does not disclose the details of their factor model. , Crouhy, Galai, and Mark . Our approach to describing KMV’s factor model is slightly different than typical presentations, because later on we will write the relevant formulas in a way supporting a convenient algorithm for the calculation of asset correlations.
An Introduction to Credit Risk Modeling by C.Bluhm, L.Overbeck & C.Wagner