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 often sparse: we have relatively few observations of the risk parameter compared to the number of covariates available. To overcome the criticism of cherry picking related to any specific model, i.e. subset of covariates, a Bayesian Model Average approach has been suggested, as in [Gross and Poblacion, 2004] 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). The advantage of this approach lies in its ease of implementation involving OLS estimates. Also from a theoretical standpoint the suggested approach can be considered an asymptotic proxy of any bayesian model for a wide class of prior distributions on the covariates parameters. Here we will test the approach proposed in [Gross and Poblacion, 2004] and [Sala-i Martin et al., 2004] against a hierarchical empirical bayesian model on both simulated and real credit risk datasets showing how the two approaches give similar results in terms of fit and forecast distribution. Nevertheless the weights associated to the sampled models can significantly differ making the bayesian model a safer choice.
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