Handling Model Uncertainty in the Estimation of Satellite Models in Bank’s Credit Risk Projections

41 Pages Posted: 18 Feb 2021 Last revised: 28 Mar 2022

See all articles by Roberto Torresetti

Roberto Torresetti

Università degli Studi di Milano; Intesa SanPaolo

Sergio Caprioli

Intesa SanPaolo SpA

Date Written: February 3, 2021

Abstract

Satellite Models are usually used by banks to project the impact of a given scenario, usually expressed in terms of macroeconomic and financial covariates, of various risk parameters, such as Loss Given Default (LGD) and Probability of Default (PD). These projections are needed in various contexts (ICAAP, Stress Testing, IFRS9 Provisioning, Recovery Plan) where usually the problem at hand is sparse: we have relatively few observations of the risk parameter compared to the number of covariates available.

A possible way to handle the model uncertainty is a Bayesian Average of Classical Estimate (BACE) approach, as in [Gross and Poblacion, 2015] and [Sala-i Martin et al., 2004], where one samples the model space and an average projection is taken weighting the sampled models in terms of a penalized likelihood as in the Bayesian Information Criterion (BIC). From a theoretical standpoint this approach can be considered an asymptotic proxy of a Bayesian model for a wide class of prior distributions as proved in [Schwarz, 1978].

Here we will test BACE against a hierarchical Bayesian model on both simulated and real credit risk data-sets following the approach of [Giannone et al., 2021]. We will present a simple JAGS implementation that can also take care of the sign constraints as usually seen in satellite models implementations and as required by the methodological note for the EBA Stress Test.

We will show how BACE can lead to significant differences of the PD projections with respect to BMA thus underlying the limits of the asymptotic approximation in BACE.

Even though in such a sparse environment it is not possible to completely eliminate any source of model uncertainty, Bayesian Model Averaging can be considered a tool to handle such risk, reducing the discretionary choices in the model identification process.

Keywords: Satellite Model, Credit Risk, Probability of Default, PD, Bayesian Estimator, Complexity Prior, LASSO, RIDGE, BIC, Model Averaging.

JEL Classification: C11, C13, C15, C51, C52

Suggested Citation

Torresetti, Roberto and Caprioli, Sergio, Handling Model Uncertainty in the Estimation of Satellite Models in Bank’s Credit Risk Projections (February 3, 2021). Available at SSRN: https://ssrn.com/abstract=3778962 or http://dx.doi.org/10.2139/ssrn.3778962

Roberto Torresetti (Contact Author)

Università degli Studi di Milano ( email )

via Festa del Perdono, 7
Milano
Italy

Intesa SanPaolo ( email )

Milan
Italy

Sergio Caprioli

Intesa SanPaolo SpA ( email )

Milan
Italy

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