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For most of the industry models it is easy to ©2003 CRC Press LLC Credit Risk Models Asset Value Models Portfolio Manager (by KMV) CreditMetrics (by RiskMetrics Group) Macroecon. 1 Today’s Best-Practice Industry Models. find some kind of technical documentation describing the mathematical framework of the model and giving some idea about the underlying data and the calibration of the model to the data. An exception is KMV’s Portfolio ManagerTM , where most of the documentation is proprietary or confidential.

6 indicate the critical thresholds or default points for each of the processes. Regarding the calibration of these default points we refer to Crosbie [19] 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 [21]. 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.

Are assumed to be uncorrelated and Additionally, the residuals δ˜ and ε ˜ We can now calculate asset correlations according independent of Γ. to (1. 29) just by computing the matrix ˜Φ ˜T E Φ ˜Γ ˜ T B T + E δ˜ δ˜ T = W BE Γ WT (1. 31) ˜ = because the matrix of standardized composite factors is given by Φ ˜ ˜ W (B Γ + δ). Let us quickly prove that (1. 31) is true. By definition, we have ˜Φ ˜T E Φ ˜ W (B Γ ˜ ˜ + δ) ˜ + δ) = E W (B Γ T ˜ ˜ T WT ˜ + δ)(B ˜ + δ) = W E (B Γ Γ ˜ Γ) ˜ T +E δ˜ δ˜ T ˜Γ ˜ T B T + BE Γ ˜ δ˜ T + E δ(B = W BE Γ = 0 WT .

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An Introduction to Credit Risk Modeling by C.Bluhm, L.Overbeck & C.Wagner

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