## Modelling Dependent Defaults (2000)

Venue: | RISK |

Citations: | 34 - 6 self |

### BibTeX

@TECHREPORT{Frey00modellingdependent,

author = {Rüdiger Frey and Alexander J. McNeil},

title = {Modelling Dependent Defaults},

institution = {RISK},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the modelling of dependent defaults using latent variable models (the approach that underlies KMV and CreditMetrics) and mixture models (the approach underlying CreditRisk+). We explore the role of copulas in the latent variable framework and present results from a simulation study showing that even for fixed asset correlation assumptions concerning the dependence of the latent variables can have a large effect on the distribution of credit losses. We explore the effect of the tail of the mixing-distribution for the tail of the credit-loss distributions. Finally, we discuss the relation between latent variable models and mixture models and provide general conditions under which these models can be mapped into each other. Our contribution can be viewed as an analysis of the model risk associated with the modelling of dependence between credit losses.

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Citation Context ... Then the distribution with mass p n k := ( ) n (−1) k n−k ∆ n−k πk on the points k/n, 1≤ k ≤ n, converges to G as n →∞. Example 5.10. There are many possibilities for generating Archimedean copulas (=-=Nelsen 1999-=-). If we take the generator φθ(t) =t −θ − 1 we get Clayton’s copula family; it may be verified that the generator inverse is a completely monotonic function. De Finetti’s theorem shows that any exchan... |

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Citation Context ... interpreted as the value of the obligor’s liabilities. Dependence between defaults is caused by dependence between the latent variables. CreditRisk + , developed by Credit Suisse Financial Products (=-=Credit-Suisse-Financial-Products 1997-=-), is, on the other hand, a typical actuarial model. In this model the default probability of a company is assumed to depend on a set of economic factors; given these factors, defaults of the individu... |

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Citation Context ...ls is given in Crouhy, Galai, and Mark (2000). The models currently in use can be divided into two classes. The models proposed by the KMV corporation (KMV-Corporation 1997) or the RiskMetrics group (=-=RiskMetrics-Group 1997-=-) are extensions of the firm-value model of Merton (1974). In these models, which are often termed latent variable models, default occurs if a latent variable, often interpreted as the value of the ob... |

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Citation Context ...description of the most popular credit risk models is given in Crouhy, Galai, and Mark (2000). The models currently in use can be divided into two classes. The models proposed by the KMV corporation (=-=KMV-Corporation 1997-=-) or the RiskMetrics group (RiskMetrics-Group 1997) are extensions of the firm-value model of Merton (1974). In these models, which are often termed latent variable models, default occurs if a latent ... |

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