| | **An Econometric Model to Quantify Benchmark Downturn LGD on Residential Mortgages**
by Marco Morone of Intesa Sanpaolo, and Marco Cornaglia of Intesa Sanpaolo May 28, 2010 **Abstract:** The paper describes a theoretical approach to determine the downturn LGD for residential mortgages, which is compliant with the regulatory requirement and thus suited to be used for validation, at least as 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 anyway be related to macroeconomic variables: in the case of mortgages, real estate prices are the common driver. Household default rates are modelled 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 years path in order to determine the loss distribution (default rates times LGD per unit of EAD), 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 DR and LGD. Some results are presented for different combinations of average LGD and unconditional possession probability, which are specific for each bank.
**JEL Classification:** C3, C32, C15, G32, C11, G21.
**AMS Classification:** 62H12, 62H20, 65C05, 68U20, 91G40, 91G70.
**Keywords:** downturn LGD, default and recovery rates correlation, mortgage, Loan to Value, real estate price, possession probability, Bayesian approach, stress testing, Vector Autoregression
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