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Statistical Risk Analysis for Real Estate Collateral Valuation using Bayesian Distributional and Quantile Regression

  • Alexander Razen


  • Wolfgang Brunauer


  • Nadja Klein


  • Thomas Kneib


  • Stefan Lang


  • Nikolaus Umlauf


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    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.

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    Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2014-12.

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    Length: 35 pages
    Date of creation: Apr 2014
    Date of revision:
    Handle: RePEc:inn:wpaper:2014-12
    Contact details of provider: Postal: Universitätsstraße 15, A - 6020 Innsbruck
    Phone: 0512/507-7151
    Fax: 0512/507-2788
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    1. Kelvin J. Lancaster, 1966. "A New Approach to Consumer Theory," Journal of Political Economy, University of Chicago Press, vol. 74, pages 132.
    2. Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
    3. Stefan Lang & Nikolaus Umlauf & Peter Wechselberger & Kenneth Harttgen & Thomas Kneib, 2012. "Multilevel structured additive regression," Working Papers 2012-07, Faculty of Economics and Statistics, University of Innsbruck.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, October.
    5. Marco Helbich & Wolfgang Brunauer & Eric Vaz & Peter Nijkamp, 2013. "Spatial Heterogeneity in Hedonic House Price Models: The Case of Austria," Tinbergen Institute Discussion Papers 13-171/VIII, Tinbergen Institute.
    6. Jeffrey P. Cohen & Cletus C. Coughlin, 2008. "Spatial Hedonic Models Of Airport Noise, Proximity, And Housing Prices," Journal of Regional Science, Wiley Blackwell, vol. 48(5), pages 859-878.
    7. McMillen, Daniel P., 2008. "Changes in the distribution of house prices over time: Structural characteristics, neighborhood, or coefficients?," Journal of Urban Economics, Elsevier, vol. 64(3), pages 573-589, November.
    8. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    11. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    12. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554.
    13. Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian Structured Additive Distributional Regression," Working Papers 2013-23, Faculty of Economics and Statistics, University of Innsbruck.
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