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.

Model risk in credit risk

Luciano E.;Semeraro P.
2020

Abstract

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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credit risk; default risk; exchangeable Bernoulli distributions; model risk; risk measures
Fontana R.; Luciano E.; Semeraro P.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1757134
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