Journal of Risk Model Validation

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An econometric model to quantify benchmark downturn loss given default on residential mortgages

Marco Morone and Anna Cornaglia

ABSTRACT

This paper describes a theoretical approach to determine the downturn loss given default (LGD) for residential mortgages, which is compliant with the regulatory requirement and thus suitable to be used for validation, not least because it can give benchmark results. The link between default rates and recovery rates is in fact acknowledged by the regulatory framework as the driver of the downturn LGD, but data constraints do not usually allow for direct estimation of such a dependency. Both default rates and LGD parameters can be related to macroeconomic variables: in the case of mortgages, real estate prices are the common driver. Household default rates are modeled inside a vector autoregressive model, incorporating a few other macroeconomic variables, which is estimated on Italian data. Assuming that LGD historical data series are not available, real estate prices influence on recovery rates is described through a theoretical Bayesian approach. Possession probability conditional to loan to value can thus be quantified, which determines the magnitude of the effect of a price increase on LGD. Macroeconomic variables are then simulated on a five year path in order to determine the loss distribution (default rates times LGD per unit of exposure at default), both in the case of stochastic price dependent LGD and of deterministic LGD (but still variable default rates). The ratio between the two measures of loss, calculated at the 99.9th percentile for consistency with the regulatory formulas, corresponds to the downturn effect on LGD. In fact, the numerator of the ratio takes into account correlations between default rate and LGD. Some results are presented for different combinations of average LGD and unconditional possession probability, which are specific for each bank.

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