On the distribution of the sum of cograduated discrete random variables with applications to credit risk analysis

Name: On the distribution of the sum of cograduated discrete random variables with applications to credit risk analysis
Brand: Vita e Pensiero
Availability: OnlineOnly

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

Title

On the distribution of the sum of cograduated discrete random variables with applications to credit risk analysis

Authors

Lucio De Capitani, Michele M. Zenga

Publisher

Vita e Pensiero

Format

Article |

Pdf

Pages

Online from

02-2016

Issn

1824-6672 (print) | 2283-6659 (digital)

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This paper focuses on the notion of cograduation which was first introduced in 1939 by the Italian statistician Tommaso Salvemini. In few words, a certain number of random variables are cograduated if they are associated with the maximum positive dependence. Here, it is shown how to derive the probability distribution of the sum of cograduated discrete random variables. This theoretical result is applied to the CreditMetrics and CreditRisk+ models in order to study the probability distribution of the value/loss of a credits portfolio under the assumption of cograduation of single credits. These applications are particularly meaningful since cograduation represents the ‘‘worst scenario’’ which is useful in order to obtain a prudential evaluation of the risk implicit in the credits portfolio.

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