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**Stress Testing: The impact of shocks on the capital needs of the Luxembourg banking sector**
by Abdelaziz Rouabah of the Banque centrale du Luxembourg, and John Theal of the Banque centrale du Luxembourg August 23, 2010 **Abstract:** We use data on loan loss provisions and total loans over the period spanning 1995 until 2009 to estimate a stress testing model for the Luxembourg banking sector. The sample encompasses the recent global crisis and covers a period in which the average probability of default of the Luxembourg banking sector's counterparties is observed to increase significantly. A joint model, consisting of several macroeconomic variables and the logit-transformed probability of default, is specified and estimated via seemingly unrelated regression (SUR). The results suggest that counterparty default rates are significantly affected by the euro area real GDP growth rate, the real interest rate and a domestic property price index. Conversely, changes in the Luxembourg real GDP growth rate have a much smaller effect on counterparty risk. We attribute this to the large number of foreign subsidiaries operating within Luxembourg. The estimated model is then used to simulate values of the probability of default and the macroeconomic variables over a horizon of 10 quarters. This allows us to construct distributions for the probability of default under both baseline and adverse scenarios. From the results of these simulations stressed Basel II tier 1 capital ratios are calculated and compared to their associated unstressed capitalization levels. Our calculations suggest that, under all the given adverse macroeconomic scenarios, the aggregate Luxembourg financial sector remains above the 4% minimum Basel II tier 1 capital requirement. Repeating the exercise on a limited sample of 5 individual banks produces similar results.
**JEL Classification:** C15, E44, G01, G21.
**Keywords:** financial stability, stress testing, Luxembourg banking sector, tier 1 capital ratio, counterparty risk
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