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Aggregating Credit and Market Risk: The Impact of Model Specification

by André Lucas of VU University Amsterdam & Tinbergen Institute, and
Bastiaan Verhoef of Royal Bank of Scotland

May 29, 2012

Abstract: We investigate the effect of model specification on the aggregation of (correlated) market and credit risk. We focus on the functional form linking systematic credit risk drivers to default probabilities. Examples include the normal based probit link function for typical structural models, or the exponential (Poisson) link function for typical reduced form models. We first show analytically how model specification impacts ‘diversification benefits’ for aggregated market and credit risk. The specification effect can lead to Value-at-Risk (VaR) reductions in the range of 3% to 47%, particularly at high confidence level VaRs. We also illustrate the effects using a fully calibrated empirical model for US data. The empirical effects corroborate our analytic results.

JEL Classification: G32, G21, C58.

Keywords: risk aggregation, credit risk, market risk, link function, diversification, reduced form models, structural models.

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