Generalized Stochastic Model of Long-Term “Cap” and “Prudent” Value Estimation

The objective of this study is to analyze existing approaches to the effect of property value fluctuations over time and develop an analytically based approach to consider its significant role. Samuelson’s Rational Theory of Warrant Pricing is used as the theoretical foundation for estimating upper (“cap”) and lower (“prudent”) property values. Analytical decisions received for the estimation of correction parameters necessary to arrive with a certain level of reliability to both the upper and lower bound of property value stochastically evolving over time. The practical application of the developed generalized methodology is demonstrated using an available residential property database. A generalized analytical approach for estimating property value lower and upper bounds is proposed and tested, combining initial market value, its general trend over time, volatility level, and required estimation reliability. The study investigates the role of these main parameters in determining the property value bounds. This research presents and describes a novel stochastic, analytically based methodology for estimating the evolving lower and upper bounds of property values over time. The results significantly contribute to existing methodologies for estimating both “prudent” and “cap” property value levels. The model development, testing, and results analysis are based on a residential property market dataset.