Determination of the trading discount based on market data and cadastral value

Abstract

The introduction of the institution of cadastral value in the Russian Federation opens up new opportunities in real estate valuation. In this regard, the new focus for appraisers is statistical analysis of multidimensional empirical distributions that were not previously available, because the real estate market does not have pairwise and multidimensional observations concentrated in unifi ed databases. Data of interest to analysts is usually concentrated in diff erent sources from diff erent owners and pertains to diff erent objects. The goal of combining them can be solved by comparing such data with the data of cadastral records, namely the cadastral number as a unique identifi er of the object. Since the cadastral value corresponds to each cadastral number, it is possible to compare the cadastral value with important indicators such as the market price of the off er, the transaction price, the rental rate, the annual price indices, the capitalization rate, the discount rate, the trading discount and many other indicators, the formation of which involves more than two random variables. The construction of the model involves the principle of following the prices formed by pair comparisons to geometric Brownian motion, and hence the formation of lognormal population. As it turned out, as a result of large-scale cadastral work carried out in the Russian Federation in 2014, the cadastral value is also subject to lognormal distribution of prices (in each class of objects). For the market value (as the most probable price of the transaction under conditions of perfect competition), this leads to functional dependences from the cadastral value of the power type. Similarly, many other indicators will also be subject to dependences in the form of power functions. Obviously, having a function depending from the various indicators of cadastral value across the set of values, you can set the relationship between the various indicators, which was impossible before the introduction of the institution of cadastral value. This article proposes a method of calculating the trading discount when appraising real estate based on analysis of market statistics and databases of cadastral records. An analytical formula of the dependence of trading discounts from the off er price is proposed. The method allows us to set the level of the discount not only for objects included in an advertising database, but also for any object that has undergone cadastral registration.

Prediction of distributions of unit prices for real estate properties on the basis of the characteristics of PSI-processes

“…Note that quantiles (in particular, median) and mode can be considered as mean values here. If this hypothesis is confirmed for any predetermined V(0) = v(0), forecast estimates can be obtained for the modal, median and mean values of the random variable V(s) using the formulas of conditional mode, median and/or conditional mathematical expectation (see, for example, [36,37]). Here, time 0 corresponds to the moment of the last observed price distribution, s is the time for which the forecast is given, its counting starts from the moment of the last observed distribution.…”