Abstract
In this paper, we analyze the impact of a decline in property prices that leads to stressed recovery rates for collateral on the loss given default (LGD) parameter in portfolios of mortgage loans. We prove that the average LGD’s stress sensitivity depends on the portfolio’s loan-to-value (LTV-) distribution and we present numerical evidence that this relationship is crucial for understanding the stress resilience of banks involved in the mortgage business. Furthermore, we derive a closed-form solution for portfolio LGD under the assumption of beta-distributed LTV-ratios and we check the robustness of this approximation for several hypothetical bank portfolios. The formula seems a meaningful starting point for benchmarking analyses by regulators, rating agencies and risk managers.
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