Page 130 - Contributed Paper Session (CPS) - Volume 1

CPS1198 Firano Z. et al.
Current value
IPHB =
2
Initial value

On the basis of this formulation, we can consider that in the absence of
real estate asset prices for future years and periods, it is possible to consider
that asset prices follow a geometric Brownian motion, where:
1
ln( ) = ln( ) + ( − ) +
2
0

2

St is the price at time t, S0 is the initial price, is the mean return and is
the volatility. The real estate’s index is:
1 2
1 ln( ) + ( − ) +
0
2
IPHB= =
0 ln( )
0

In this sense, it is necessary to estimate the three main parameters, the
price according to the hedonic model, the average of the returns and the
volatility. Thus, and in order to determine the value of real estate price returns,
we have resorted to the theory of prices in the financial markets, including real
estate markets. We know that prices are determined by their intrinsic value, so
are the economic determinants of price that can explain its evolution,
according to Euler's training we can write that:

P = ( + +1 ) (1.1)
+1

With: = 1⁄(1 + ) is discount factor and is discount rate. If one adopts
the fundamental design of the Muth, (1961) rationalized asset price evaluation,
and accepts that the transversally condition is satisfied, then the fundamental
value is considered the only solution to the valuation problem of asset prices:

∗
= ∑ + (1.2)
0
=1

is the fundamental value. Thus, we can write:
∗
0

∗
= ∑ + = ∑ .

,

=1 =1

Then the coefficients estimated in the hedonic equation, all else being
equal, describe the factors of actualization.
In general, the estimation method adopted in hedonic models is ordinary
least squares, since the model is generally linear and satisfies the required
conditions. However, real estate is of a specific nature where the valuation of
property depends on several parameters in addition to the intrinsic

2 IPHB: Brownian hedonic price index
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