Estimation of Joint Credit Losses Based on Poisson Processes and a Suggestion for Basel Accords

This paper suggests a model based on Poisson processes to estimate joint credit losses without the limitations of normality assumptions and non-negative correlation. Idiosyncratic and systematic risks are seen as “shocks” and defaults are driven by a latent variable (loans' lifetimes). The method is applied to the calculation of capital to cover unexpected credit losses in financial institutions and a simple expression is proposed to replace the “Vasicek formula” employed nowadays to estimate potential losses in adverse scenarios. Simulations show that the general model yields satisfactory estimations of simultaneous credit losses and its application to capital assessment outperforms the current approach (Basel II) for non-normally distributed losses even when the alternative method is calculated at lower levels of confidence (95%, while Basel adopts 99.9%). In general, for portfolios presenting beta, exponential, and gamma default distributions, Basel II formula underestimated the maximum losses whilst the alternative model yielded more precise results with small overestimation. Therefore, considering the higher accuracy and easy implementation of the Poisson method, it may be used in bank regulation in order to avoid underestimation of credit losses in downturns especially when they are not normally distributed. Moreover, another interesting property of this model is the possibility of capturing negative correlations (although they are seldom observed in reality) such that the final risk can incorporate this potential benefit of diversification for lenders. As a next step to the consolidation of this suggested formula, it should be tested in datasets of financial institutions and then its results may be compared to Basel calculations