Statistical risk analysis for real estate collateral valuation using Bayesian distributional and quantile regression

The Basel II framework strictly defines the conditions under which financial institutions are authorized to accept real estate as collateral in order to decrease their credit risk. A widely used concept for its valuation is the hedonic approach. It assumes, that a property can be characterized by a bundle of covariates that involves both individual attributes of the building itself and locational attributes of the region where the building is located in. Each of these attributes can be assigned an implicit price, summing up to the value of the entire property. With respect to value-at-risk concepts financial institutions are often not only interested in the expected value but also in different quantiles of the distribution of real estate prices. To meet these requirements, we develop and compare multilevel structured additive regression models based on GAMLSS type approaches and quantile regression, respectively. Our models involve linear, nonlinear and spatial effects. Nonlinear effects are modeled with P-splines, spatial effects are represented by Gaussian Markov random fields. Due to the high complexity of the models statistical inference is fully Bayesian and based on highly efficient Markov chain Monte Carlo simulation techniques.