This paper analyzes the unconditional measurement of default risk and proposes an alternative modeling approach. We begin the analysis by showing that when conducted under non-stationarity, the objective of the unconditional measurement changes and that some relevant problems appear as a consequence of the sample dependence. Based on this result, we introduce our approach and discuss its consistency, practical advantages, and the main differences from the conventional static framework. An empirical analysis is also conducted. Under nonstationarity, the regulatory model for the unconditional probability of default distribution performs badly when compared to our approach. Results also show that the capital figure presents a determinant and nontrivial dependence on the homogeneity and severity of the economic scenario represented in the sample. We begin the analysis by showing that when conducted under non-stationarity, the objective of the unconditional measurement changes and that some relevant problems appear as a consequence of the sample dependence. Based on this result, we introduce our approach and discuss its consistency, practical advantages, and the main differences from the conventional static framework. An empirical analysis is also conducted. Under non-stationarity, the regulatory model for the unconditional probability of default distribution performs badly when compared to our approach. Results also show that the capital figure presents a determinant and non-trivial dependence on the homogeneity and severity of the economic scenario represented in the sample.

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This paper addresses two problems related to determining the unconditional capital required by a credit portfolio: Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter. Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter.

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