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Model risk in credit risk
Author(s) -
Fontana Roberto,
Luciano Elisa,
Semeraro Patrizia
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12285
Subject(s) - bernoulli's principle , mathematics , dimension (graph theory) , value at risk , credit risk , econometrics , random variable , class (philosophy) , risk measure , expected shortfall , measure (data warehouse) , economics , statistics , mathematical economics , risk management , combinatorics , actuarial science , computer science , financial economics , finance , physics , portfolio , artificial intelligence , thermodynamics , database
We provide sharp analytical upper and lower bounds for value‐at‐risk (VaR) and sharp bounds for expected shortfall (ES) of portfolios of any dimension subject to default risk. To do so, the main methodological contribution of the paper consists in analytically finding the convex hull generators for the class of exchangeable Bernoulli variables with given mean and for the class of exchangeable Bernoulli variables with given mean and correlation in any dimension. Using these analytical results, we first describe all possible dependence structures for default, in the class of finite sequences of exchangeable Bernoulli random variables. We then measure how model risk affects VaR and ES.

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