AHP and Nonlinear Optimization to Improve Market-Value Appraisal of Real Estate Assets

In real estate appraisal, the market value of a property is often identified based on the principle of price equilibrium; thus, the prices of similar, recently traded real estate assets are the basis for the assessment. Under this framework, a technique widely used by practitioners and appraisers goes under the name of sales comparison adjustment grid. The property to be assessed (the so-called subject) is compared to ten or so transactions (the so-called comparables). Adjustments are made to the comparables’ prices to reflect their di erences with respect to the subject. To that end, the properties’ main attributes - namely, the features the market players on the demand and supply side value the most - must be listed and weighted. The weighting of the attributes - usually based on the appraisers’ local real estate market knowledge - is among the most prominent weaknesses of the appraisal technique. We propose to improve it by deriving the weights from the data itself using a model combining the methodological setting of the Analytic Hierarchy Process (AHP) and nonlinear optimization. On the one hand, a ranking of the comparables is derived by the pairwise comparison of their prices. On the other hand, another ranking is derived by the pairwise comparison of their attributes. The weights of the attributes are then iteratively searched as those that minimize the distance between the two rankings.