Real Options Premia Implied from Recent Transactions in the Greek Real Estate Market

Article

Abstract

This research is the first to examine the empirical predictions of a real option-pricing model on market values from the realty market of a Euro area country, namely Greece. Using a manually collected sample of land and property transaction prices, we demonstrate that, a model which incorporates the option to wait to develop land has explanatory power on observed prices over and above the intrinsic value from a simple discounted cash flow (DCF) approach. Recent land transactions in our sample seem to reflect a premium for the option to wait (‘real option premium’) that can be as high as 26.66%–52.38%, especially in the west and north suburbs of Athens. Estimates of annual volatility for specific properties, as implied by transaction prices, are found to range from 15% to 21%.

Keywords

Real options Urban land values Greek real estate Development 

JEL Classification

G13 R33 

Introduction

The empirical performance of alternative option-pricing models for financial assets has been extensively tested and reported in the literature. In contrast, less research has concentrated on the empirical record of option-based valuation models for real assets.

Although the “real options” literature has offered a plethora of theoretical models for the valuation of real assets (Titman 1985; Brennan and Schwartz, 1985; McDonald and Siegel, 1985 and 1986, among others; see Dixit and Pindyck 1994, for a review), empirical and applied studies have been few and far between, primarily focused on natural resource investments (Paddock et al. 1988; Moel and Tufano 2002) and urban land valuation (Quigg 1993; Grovenstein et al. 2011).

This short paper contributes to this literature by being the first that examines the empirical predictions of a real options model, using a fairly large sample of recent transactions from the Greek real estate market. Previous empirical investigations of real options in land values have concentrated mainly in the U.S. market. To the best of our knowledge, this is the first study that employs micro-level, real estate transaction data from a euro area member country to provide evidence for real options in land prices.

In order to accomplish this, we employ an infinite horizon, continuous time model that follows the work of Williams (1991), and is also used by Quigg (1993) and Grovenstein et al. (2011) in their empirical investigations of land values in the U.S.A. (Seattle and Cook County respectively). The model allows us to compare the option-based value of land (that incorporates the option to wait to develop), with its intrinsic value and its price in the market. These “real option premia” are found to be significant in magnitude, ranging from 26.66 to 52.38%, with a mean of 36% across all sample observations. On average, the highest premia are associated with transactions in the north and west suburbs of Athens, suggesting that land purchases in these areas have been more speculative in nature during the time period under review.

Moreover, we find that the option-based values have superior power in explaining observed land transaction prices, over and above the intrinsic value from a simple discounted cash flow (DCF) approach. The immediate implication is that real estate models, especially those concerned with the valuation of land, should account for the (real) option to wait, if one believes that property development investments can be optimally timed, at least partly, at will.

Finally, we provide estimates of implied standard deviations of individual housing properties in the region of 15 to 21% per annum. These are comparable to-if not slightly lower than-estimates reported in earlier studies by Quigg (1993), Yamaguchi et al. (2000) and Holland et al. (2000). As Quigg (1993, p. 622) points out, the calculation of such implied standard deviations “is a contribution in itself, as a lack of repeat sales data for this class of assets makes it difficult to estimate the price variance directly”; this is especially true for a shallow real estate market like Greece.

Our paper is mostly related to the work of Quigg (1993), Yamaguchi et al. (2000), Sing and Patel (2001) and Grovenstein et al. (2011). All the aforementioned studies apply virtually the same model to land transactions from different real estate markets (Seattle, U.S.; Japan; U.K. and Cook County, U.S. respectively). This is the first study that examines the empirical predictions of a real option-pricing model on market values from the realty market of a euro area country. Yavas and Sirmans (2005) use laboratory experiments to generate the data on which the fundamental premises of real options theory are tested. Also related are papers by Holland et al. (2000), Cunningham (2006) and Bulan et al. (2009), that apply reduced-form hazard models in their examination of the relationship between volatility and irreversible investment in real estate development. However, our objective in this paper is to examine whether the option to wait to develop property is actually present in observed land prices in the Greek market, and not on testing the effect of uncertainty on the timing of development that is the main focus of the aforementioned studies.

Important theoretical contributions in the intersection of real estate and real options theory have been offered by Capozza and Sick (1991), Capozza and Li (1994), Geltner et al. (1996), Grenadier (1995, 1996), Bar-Ilan and Strange (1996) and Lee and Jou (2010), among others.

The rest of the paper is organized as follows: The next section provides some background information regarding the realty market in the Hellenic Republic. The section that follows it describes the land transactions data set, while the next section presents the theoretical real options model. The following section discusses a number of methodological issues that are intermediate phases in the empirical investigation of the model, while the next one presents and discuses the empirical results. The last section concludes the paper.

Greek Realty: Background Information

This section provides some relevant background information regarding the Hellenic Republic (Greece) and its real estate market. It is intended mainly for the benefit of readers unfamiliar with the country’s administrative divisions and demographics, so that the nature of our data set can be better understood.

Greece has a total area of 131,940 km2, of which 130,800 km2 is land area (The World Fact book 2008). Administratively, the country consists of 13 peripheries (see Fig. 1); Central Macedonia is the largest (18,811 km2, no. 3 in Fig. 1) and the Ionian islands the smallest (2,307 km2, no. 7).
Fig 1

The 13 peripheries of the Hellenic Republic. Source: Wikipedia commons

The periphery of Attica (no. 1 in Fig. 1), that contains the capital Athens, covers only 2.9% of the country’s total surface (3.808 km2); however it is occupied by 34.3% of the total population (3.77 million citizens, as of 2001). The periphery of Attica consists of four prefectures: Athens, East Attica, Piraeus and West Attica (see Fig. 2). The Athens prefecture (no. 1) is the most densely populated, with 7,376 inhabitants/km2, followed by Piraeus (no.3, with 583 inhabitants/km2), East Attica (no.2, with 276 inhabitants/km2) and West Attica (151 inhabitants/km2). Our data set consists of manually-collected, land and housing property transactions from the periphery of Attica, with no transactions however from the thinly populated West Attica prefecture.
Fig. 2

The periphery of Attica and its four prefectures: Athens (no. 1), East Attica (no. 2), Piraeus (no. 3) and West Attica (no. 4). Source: Wikipedia commons

Although the actual value of real estate in Greece is hard to estimate due to data unavailability, many estimate it close to half a trillion euros, more than the country’s annual GDP (approx. 300 billion euros). Furthermore, on average, 1.5% of the annual growth rate of the economy derives from real estate transactions (sales and purchases). Greece has one of the highest (79.9%) ownership percentages in the world. It is 71.1% in urban areas, in semi-urban areas 87.6%, and in agricultural areas 97% (see the real estate industry study by the ICAP Group, 2007).

The preparation for the summer Olympic Games in Athens in 2004 has given a boost to the real estate market and construction industry. This boom had positive repercussions in the years that followed. Furthermore, the market was boosted in 2005 when the government announced measures to be introduced in 2006, such as VAT on new constructions. Stability characterized the first 6 months of 2006, while there have been increasing trends in the second half of 2006 and the first half of 2007. Since the summer of 2007, the ensuing financial crisis has affected the market tremendously: low mortgage financing, virtually no transactions, and prices falling 10–15% in recent months. Our transactions in this paper are from 2004 to 2007, with most of them in 2006 and 2007, thus the effect of the global financial crisis should be limited. The section that follows described the data in more detail.

Sample of Vacant Land Transactions

We have manually collected 631 recent vacant land sales in Attica; these account for roughly 3% of all transactions in any year, and come from major real estate brokers such as RE/MAX Hellas, Aspis Real Estate, Greek Estate, Denaro, and others.

We classify land parcels into five distinct zone categories, labeled ‘centre’, ‘east’, ‘south’, ‘west’ and ‘north’, and associate them with dummy variables 1 to 5 respectively. The classification can be visualized with the aid of Fig. 3. There are altogether 27, 298, 247, 11 and 48 recent vacant land transactions in our sample, in the ‘centre’, ‘east’, ‘south’, ‘west’ and ‘north’ zone categories respectively. Their classification by municipality is summarized in Table 1. It is obvious that some areas, especially in the ‘east’ zone (e.g. Paiania, Porto Rafti, etc.) are over-represented in our data set.
Fig. 3

Zone categories in the Attica periphery

Table 1

Vacant land transaction data, categorized by municipality

Municipality

No. of Obs.

Dummy

Municipality

No. of Obs.

Dummy

Neo Irakleio

1

5

Keratea

11

3

Agia Marina

1

3

Kifisia

4

5

Agia Paraskevi

11

5

Koridallos

1

4

Agios Dimitrios

3

1

Kropia

89

3

Agios Stefanos

1

5

Lagonisi

10

3

Athens

24

1

Laurio

11

3

Alimos

2

3

Magoula

1

4

Anavissos

9

3

Marathonas

5

2

Anthousa

4

2

Markopoulo Mes.

49

3

Anoixi

1

5

Marousi

1

5

Melissia

1

5

Menidi

2

3

Artemida

5

2

Metamorfosi

1

5

Vari

3

3

Psihiko

1

5

Varkiza

1

3

Nea Erithraia

2

5

Varnavas

4

2

Nea Penteli

1

5

Varibobi

1

2

Nea Smirni

1

1

Voula

3

3

Nea Filadelfia

2

1

Vravrona

11

2

Neo Faliro

1

3

Vrilisia

1

5

Paiania

132

2

Vironas

1

1

Palaio Faliro

1

3

Gerakas

15

2

Palaio Psihiko

1

5

Glika Nera

31

2

Pallini

33

3

Glifada

1

3

Piraeus

4

3

Dionisos

2

5

Penteli

3

5

Ekali

2

5

Perissos

1

1

Zografou

1

1

Peristeri

2

4

Kaisariani

1

1

Pikermi

13

2

Kalivia

15

3

Porto Rafti

43

2

Kamatero

2

4

Rafina

6

2

Kaminia

1

4

Saronida

1

3

Kapandriti

3

5

Spata

27

2

Cholargos

1

5

Stamata

1

5

Chalandri

7

5

   
Table 2 reports useful descriptive statistics of the vacant land transactions in our sample. The largest land parcels in our sample are found in the north and in the south suburbs, while the highest prices are paid for land in the north and in the centre. The former is due to the fact that northern suburbs are traditionally highly priced. The latter might be due to the fact that land parcels in the centre are associated with limited availability and higher construction factors on average.1 The individual land transaction prices in our sample range from slightly above 20 thousands euros to over 50 million.
Table 2

Descriptive statistics of vacant land transaction data

Regions

Construction factor

Coverage factor

Size (m2)

Price (€)

Average

Average

Min.

Max.

Centre

2.07

0.52

1,439

1,805,333

105,000

13,206,000

East

0.71

0.30

3,726

616,751

22,000

14,675,000

South

0.85

0.33

8,126

1,038,211

20,542

25,000,000

West

0.91

0.37

906

895,000

110,000

5,500,000

North

0.84

0.34

21,784

2,328,557

161,500

52,900,000

The Model

The model we employ is directly adapted from the empirical investigation by Quigg (1993) and Grovenstein et al. (2011) on land transactions in the U.S. It is an infinite-horizon, continuous time model that is based on the work of Williams (1991) and the predictions of Titman (1985).

The owner of a land parcel (the investor) holds a perpetual option to develop a building on it, at an optimal date and density, subject to land policy (as the latter is dictated by the state through civil planning regulations). Land ownership is thus valued as a ‘real option’, i.e. an option-without the corresponding obligation-to time the development of an optimally sized building. However, in order to follow this approach, one needs to know the value of the building that will be developed in the future (the ‘underlying asset’), upon exercise of the ‘option to develop’; since this asset is unobservable, this poses a great difficulty in applying the ‘real options’ approach.

In outlining the model below we keep the notation in Quigg (1993) for ease of correspondence between her and our results. Assume that the cost of the building is a linear function of fixed, f and variable x1 development costs, expressed as
$$ X = f + {q^{\gamma }}{x_1}, $$
(1)
where q are the square meters of the building, x1 is the development cost per square meter, and γ is the cost elasticity of scale.
The cost of development evolves stochastically through time according to a geometric Brownian motion, with a constant drift ax and a constant variance \( \sigma_x^2 \):
$$ dX = {a_x}Xdt + {\sigma_x}Xd{z_x} $$
(2)
Assume, for the purpose of developing the model that the price P of the building, i.e. the underlying asset of the option to develop, is observable, and it follows a geometric Brownian motion
$$ dP = \left( {{a_p} - {x_2}} \right)Pdt + {\sigma_p}Pd{z_p} $$
(3)
with constant drift and variance. In Eq. 3, x2 denotes any payouts to the developed building, and the increments dzp are allowed to be correlated with dzx, with a constant correlation ρ per unit of time dt.
Moreover, the time-varying price of the building can be expressed, at any point in time, as
$$ P = {q^{\varphi }}\varepsilon $$
(4)
with q as before, φ the price elasticity of scale, and ε a functional expression of all other attributes of the building (apart from size q) that contribute to its price.2 As in Quigg (1993), we require that the cost elasticity of scale γ exceeds φ, the price elasticity of scale.

In order to derive V(X, P), the value of undeveloped property, we assume that there is an equilibrium in which any claims contingent on the pair of stochastic processes X, P for the development cost and building price are uniquely price. This is similar to the equilibrium derived in Rubinstein (1976). As in Quigg (1993), we further assume that (a) land owners are price-takers, i.e. the decision to develop by an individual land owner has no effect on the market value of buildings, (b) there is a constant, instantaneous risk-free interest rate that equally applies to borrowing and lending, and (c) the undeveloped property earns proportional payouts, βP, before development, and the decision to develop is irreversible.

Under these assumptions, the value of the undeveloped property, V(X, P) can be expressed as the solution to the following second-order, partial differential equation
$$ \frac{1}{2}\sigma_x^2{X^2}{V_{{xx}}} + {\sigma_{{xp}}}XP{V_{{xp}}} + \frac{1}{2}\sigma_p^2{P^2}{V_{{pp}}} + {v_x}X{V_x} + {v_p}P{V_p} - iV + \beta P = 0, $$
(5)
where i is the constant instantaneous risk free rate, νxaxλxσx and \( {\nu_p} \equiv ({a_p} - {x_2}) - {\lambda_p}{\sigma_p} \) the risk-adjusted drifts and λp (λx) the market price of the risk that is associated with the uncertainty in the property price (construction cost), per unit of standard deviation. Parameter \( {\nu_p} \equiv ({a_p} - {x_2}) - {\lambda_p}{\sigma_p} \) denotes the covariance of changes in X and P.
Since the value of the undeveloped property V(X, P) is homogenous of degree one in X, P, the problem can be simplified by making the change of variable zP/X. One obtains W(z) ≡ V(X, P)/X and
$$ \frac{1}{2}{\omega^2}{z^2}W\prime \prime + \left( {{v_p} - {v_x}} \right)zW\prime + \left( {{v_x} - i} \right)W + \beta z = 0, $$
(6)
where \( {\omega^2} = \sigma_x^2 - 2\rho {\sigma_x}{\sigma_p} + \sigma_p^2 \) is the instantaneous variance of z.
This change of variable essentially implies that there is a ratio of building market price to development cost, z*, at which it is optimal to immediately build on vacant land. The solution to the valuation problem is given by (see Appendix for a detailed derivation):
$$ V\left( {X,P} \right) = X\left( {A{z^j} + k} \right) $$
(7)
where,
$$ A = \left( {{z^{ * }} - 1 - k} \right){\left( {{z^{ * }}} \right)^{{ - j}}} $$
(8)
$$ {z^{ * }} = \frac{{j\left( {1 + k} \right)}}{{j - 1}} $$
(9)
$$ k = \frac{{\beta z}}{{i - {\nu_x}}} $$
(10)
$$ j = {\omega^{{ - 2}}}\left\{ {\frac{1}{2}{\omega^2} + {v_x} - {v_p} + {{\left[ {{\omega^2}\left( {\frac{1}{4}{\omega^2} - {v_p} - {v_x} + 2i} \right) + {{\left( {{v_x} - {v_p}} \right)}^2}} \right]}^{{\frac{1}{2}}}}} \right\}. $$
(11)

If the ratio of building market price to development cost z exceeds z*, the land owner finds it optimal to exercise her ‘real option’ to develop immediately. The land owner will only find it optimal to immediately exercise, if the ratio zP/X exceeds the ‘hurdle rate’ 1+k (that corresponds to holding the land for the income it generates, see Eq. 10) by a factor \( \frac{j}{{j - 1}} > 1 \) (since j > 1). This factor, that represents the ‘real option value of waiting’ and is related to Tobin’s (1969) q measure, is known to be increasing in ω, the volatility of the ratio z, the risk free rate i, and the intrinsic value of this option (see Dixit and Pindyck 1994).

The intrinsic value of this real option to wait to develop can be determined by taking the limit, as the volatility goes to zero, ω→0, of Eq. 10. This is equal to
$$ {V^I}\left( {X,P} \right) = \left\{ {\begin{array}{*{20}{c}} {P - X,} \hfill & {{\text{if}}\;z \geqslant 1 + k} \hfill \\ {\frac{{\beta P}}{{i - {\nu_x}}},} \hfill & {{\text{if}}\;z < 1 + k} \hfill \\ \end{array} } \right. $$
(12)

This is essentially the discounted cash flow (DCF), net present value of the investment to develop.

In the empirical section of the paper, land values, given by the real option model of Eq. 7, are compared to the intrinsic, DCF values in (12) and the observed transaction prices. However, applying Eq. 7 requires knowledge of P, the price of the building that will be developed, and q, the scale of the building that potentially would be developed. Both are unobservable, but can be estimated through market data. This is what we turn to in the section that follows.

Underlying Building Estimates: Data, Methodology and Results

In order to evaluate land as an option, for which the underlying asset is the property that would be developed on the site, we need to estimate the potential price of this hypothetical building. To this end, we employ hedonic estimation, a method that focuses on determining a price function for a general product/commodity that embodies-at various degrees-a number of characteristics or attributes Ψ. A hedonic price function P(Ψ), essentially describes how the price of a product/commodity varies as the attributes Ψ vary. Rosen (1974) is the primary reference for the theoretical foundations of the method, while Bartik and Smith (1987) and Palmquist (1991) review real estate related applications of the method.

A. Sample of Property Transactions

We base our hedonic estimation on a sample of manually-collected housing property transactions in the Attica prefecture, obtained from the same real estate brokers as the land transactions that are described in Sample of Vacant Land Transactions section. We employ the same 5-zone categorization of Fig. 3 (‘centre’, ‘east’, ‘south’, ‘west’ and ‘north’), and present all property transactions by municipality in Table 3. The majority of building transactions in our sample are from the ‘centre’ (78 observations), followed by transactions in the ‘north’ and ‘south’ regions.
Table 3

Property transaction data, categorized by municipality

Municipality

No. of Obs.

Dummy

Municipality

No. of Obs.

Dummy

Agia Varvara

4

4

Vrilissia

6

5

Ag. Paraskevi

12

5

Vyronas

4

1

Maroussi

4

5

Zografou

1

1

Athens

52

1

Agios Stefanos

7

5

Chalandri

5

5

Artemis (Loutsa)

4

3

Cholargos

11

5

Gerakas

18

2

Dafni

1

3

Glyka Nera

12

2

Ekali

1

5

Kropia

1

2

Filothei

1

1

Marathon

2

3

Galatsi

2

1

Markopoulo Mes.

1

2

Glyfada

1

3

Pallini

5

2

Irakleio

1

5

Spata

1

2

Kaisariani

2

1

Vari

1

1

Kallithea

2

1

Voula

2

3

Kifissia

5

1

Anavyssos

1

3

Melissia

2

5

Anoixi

3

5

Nea Erythraia

1

5

Dionysos

2

5

N. Filadelfeia

1

1

Drosia

2

5

Nea Smyrni

2

1

Kryoneri

1

5

Nea Penteli

1

5

Palaia Fokaia

1

3

Neo Psychiko

3

5

Saronida

6

3

Palaio Faliro

3

3

Stamata

2

2

Pefki

3

5

Thrakomakedones

1

5

Peristeri

14

4

Piraeus

5

3

Petroupoli

3

4

Perama

1

3

Nikaia

18

3

Koridallos

11

4

Keratsini

4

3

   
Table 4 reports descriptive statistics of the property transactions. As the Table suggests, sales in the ‘centre’ region are associated-on average-with older (19.21 years), smaller (92.45 m2), higher (2.88 floors) and more densely-constructed buildings. Properties in the ‘east’ are on average newer (1.05 years) and less densely-constructed. Housing properties appear most expensive in the ‘north’ and ‘south’ regions of Attica in our sample (on average, 491,069 € and 372,754 € respectively), while they appear least expensive in the ‘west’ (164,912 €).
Table 4

Descriptive statistics of property transaction data

Regions

Construction factor

Height (floors)

Size (m2)

Age (years)

Price (€)

Average

Average

Min.

Max.

Centre

2.80

2.88

92.45

19.21

181,923

15,000

310,000

East

0.74

1.49

139.18

1.05

309,817

124,800

980,000

South

1.54

2.51

141.02

7.77

372,754

55,000

6,700,000

West

1.59

1.59

99.16

16.97

164,912

32,000

280,000

North

0.78

1.78

174.17

8.03

491,069

110,000

2,950,000

B. Hedonic Estimation

We use the hedonic model because of the heterogeneity that characterizes the buildings in our sample, as described in the previous section. The general model we estimate is a modified version of the quadratic Box-Cox functional form
$$ {P^{{\left( \theta \right)}}} = {h_0} + \sum\limits_i^n {{h_i}{\Psi_i} + \frac{1}{2}\sum\limits_i^n {\sum\limits_j^n {{\varphi_{{ij}}}{\Psi_i}{\Psi_j} + \sum\limits_r^4 {{\xi_r}{L_r},} } } } $$
(13)
where P is the property transaction price, Ψi are the available characteristics or attributes of the building, i.e. age, height, size, etc., Lr are four location dummy variables (‘east’, ‘south’, ‘west’ and ‘north’; the ‘centre’ location dummy is the eliminated variable in the estimation), and P(θ) is a Box-Cox transformation
$$ {P^{{\left( \theta \right)}}} = \left\{ {\begin{array}{*{20}{c}} {\frac{{{P^{\theta }} - 1}}{\theta },} \hfill & {{\text{for}}\;\theta \ne 0} \hfill \\ {\ln P,} \hfill & {{\text{for}}\;\theta = 0} \hfill \\ \end{array} } \right. $$
(14)

The appropriateness of (13) stems from the fact that it nests a number of hedonic price functional forms that have been proposed in the literature as special, restricted cases (e.g. linear, quadratic, square root quadratic, translog, etc., see Halvorsen and Pollakowski, 1981 for details).

We estimate Eq. 13 stepwise, for all possible combinations, and keep the specification whose Box-Cox transformation provides the highest log likelihood and lowest standard error. This is
$$ \ln {P_i} = {h_0} + \varphi \ln {q_i} + {h_1}H{T_i} + {h_2}AG{E_i} + {h_3}HT_i^2 + \sum\limits_r^4 {{\xi_r}{L_{{r,i}}} + {e_i}} $$
(15)
with qi the size of property i, HTi the height of the building in floors, AGEi its age measured in years and the location dummies Lr,i as defined earlier. Estimation results are summarized in Table 5.
Table 5

Hedonic estimation for property transaction data

Adj. R2

0.9036

log L

−395.91

RMSE

1.8296

No of Obs.

276

Variable

Coefficient

Std. error

Constant

3.2809

0.2198

ln q

0.7199

0.2985

AGE

−0.0109

0.0030

HT

0.4503

0.0918

HT2

−0.0567

0.0202

Location, Lr

Centre

0

 

East

3.7407

0.2650

South

3.8795

0.1697

West

3.7527

0.1904

North

4.0002

0.1313

The fit of the specification is very good, with an adjusted R2 of 90.36%. This is comparable to the coefficients of determination reported in Quigg (1993) for properties in Seattle, U.S., but significantly higher than those in Grovenstein et al. (2011) for Cook County, U.S.

All coefficient estimates are statistically different from zero, even at the α = 1% significance level. The price elasticity of size, φ is 0.7199, with a standard error of 0.2985. Although this is obviously statistically different from zero, one cannot reject the hypothesis that φ>1 at conventional levels. The estimate of φ is significantly higher than those reported in Quigg (1993) and Grovenstein et al. (2011) for the U.S.; however the estimate is associated with a fairly high standard error, making conclusive comparisons with U.S. estimates difficult.

The age and the height (number of floors) are found to contribute significantly to the explanatory power of the specification, the latter variable in a non-linear fashion (with an increasing effect, at a decreasing rate). The coefficient of AGEi is significantly lower (more negative) than the corresponding coefficients reported in Quigg (1993) and Grovenstein et al. (2011) for residential properties in the U.S.

From the coefficient estimates of the location dummies, one can infer that Attica is rather monocentric, since the distance from the ‘centre’ is associated with positive price effects. Property prices in the ‘north’ and ‘south’ suburbs are found to attract higher prices.

We use the estimates of Table 5 to predict the building prices that would correspond to each vacant land parcel in our sample, if valued as a real option. From Eq. 4, the price of the building (underlying price) is P = qφε, where φ is the price elasticity of size as in the hedonic price model (15), and ε is a function of other attributes of the building. However, in order to apply this, one needs to estimate the height and the size of the building that would be developed. For the former, we follow Quigg (1993) and set the estimated height for the building, \( \widehat{{HT}} \), equal to the average height of existing properties in the relevant zoning area. These are reported in Table 4. For the size, we infer its optimal level for the building that will be developed by maximizing the value of the undeveloped land parcel, \( V(q) = P - X = {q^{\varphi }}\varepsilon - \left( {f + {q^{\gamma }}{x_1}} \right) \) over q. The solution is
$$ {q^{ * }} = \left\{ {\begin{array}{*{20}{c}} {{{\left( {\frac{{\gamma {x_1}}}{{\varepsilon \varphi }}} \right)}^{{\frac{1}{{\varphi - \gamma }}}}},} \hfill & {{\text{for}}\;{q^{ * }} < \delta } \hfill \\ {\delta, } \hfill & {{\text{for}}\;{q^{ * }} \geqslant \delta } \hfill \\ \end{array} } \right. $$
(16)
where δ is the maximum-allowed by zoning regulations-size that can be constructed (see Grovenstein et al. 2011).
Thus, for each of the 631 land transactions in our sample, we calculate an estimated value for the building that would be developed, by
$$ {P_i} = {\left( {q_i^{ * }} \right)^{\varphi }}\widehat{\varepsilon } = {\left( {q_i^{ * }} \right)^{\varphi }}\exp \left\{ {{h_0} + {h_1}{{\widehat{{HT}}}_i} + {h_3}\widehat{{HT}}_i^2 + \sum\limits_r^5 {{\xi_r}{L_{{r,i}}}} } \right\} $$
(17)
with L the actual location of the land parcel.

Land Value Real Options Model: Results

For each zoning category, we evaluate real option values of vacant land via Eq. 7, using Eq. 17 to determine the value of the underlying building. In order to apply the valuation model, we assume that the risk-adjusted parameters are νp = νx = 0.03 and the risk-free interest rate i = 0.05.

Moreover, we need to assume values for the development cost scale parameter, γ, and the payout to the undeveloped property β. Since theory and prior research do not dictate specific choices, we assume values that minimize pricing errors in our sample. For γ, these range from 0.9 to 1, while for β from 1% to 4%. These assumptions are all comparable to those made by Quigg (1993) in her investigation.

The theoretical values we calculate are found to be most sensitive to the assumption regarding the development cost scale parameter, γ, and almost insensitive to the assumptions for νp, νx and i. Fortunately, both real option and intrinsic values are equally affected by the building price P, development cost X, building size q* and estimates γ and β. Thus, any changes to, or estimation errors in, these parameters should not alter significantly any conclusions drawn by comparisons of option and intrinsic values.

We infer estimates of volatility, as implied from the real options model of land value. We first calculate the standard deviation of the developed property value and construction costs, i.e. the parameters ω that equate theoretical land values from Eq. 7 to market values in our sample. Estimates, averaged across observations in each location zone, are reported in Table 6. These are found to be substantial in magnitude, with very low standard errors.
Table 6

Volatility estimates implied from the real options model

Region

Implied volatility \( \omega = \sqrt {{\sigma_x^2 - 2\rho {\sigma_x}{\sigma_p} + \sigma_p^2}} \)

Implied volatility σp

Average

St. error

Min.

Max.

Average

St. error

Min.

Max.

Centre

0.16

0.0137

0.05

0.22

0.15

0.0163

0.02

0.21

East

0.18

0.0030

0.05

0.21

0.17

0.0036

0.00

0.20

South

0.17

0.0038

0.05

0.22

0.16

0.0047

0.00

0.23

West

0.21

0.0139

0.05

0.21

0.21

0.0168

0.02

0.24

North

0.18

0.0084

0.05

0.21

0.17

0.0103

0.00

0.21

We proceed to calculate estimates of the implied volatility of the developed property value only, i.e. σp, assuming σx = 0.05 and ρ = 0. Annual volatilities are found to range between 15% and 21%, with only slight differences across zoning areas. Land transaction prices in the West areas of the Attica prefecture seem to be associated with idiosyncratic risk levels above the average in our sample (21% as opposed to 16%, the average across all transactions). Comparable estimates in the literature can be found in Quigg (1993)—ranging between 18% and 28% for transactions in Seattle in the 1977–1979 period—in Yamaguchi et al. (2000)—ranging between 18.5% and 36.5% for transactions in Tokyo in the 1986–1993 period—and in Holland et al. (2000)—ranging between 15% and 25%. It seems that the idiosyncratic risk levels inherent in recent prices of land in Greece are lower than those reported in other countries.

Moreover, we calculate price differences between the option-based model and the intrinsic values. In Table 7 we report real option premia, calculated as the mean percentage difference between the real options price and the intrinsic value, i.e.
Table 7

Real options (wait to develop) premia

Region

Option value (€)

Intrinsic value (€)

Option premium

Centre

4,367,664

2,106,391

26.66%

East

1,363,246

990,416

27.82%

South

4,237,388

2,299,235

35.88%

West

1,163,023

939,683

36.50%

North

6,580,036

2,512,800

52.38%

$$ \frac{{V\left( {X,P} \right) - V^I\left( {X,P} \right)}}{{V\left( {X,P} \right)}}. $$
(18)

These should reflect price premia (if any) for the option of waiting to invest (optimal development). In accordance with theory, real options premia are positive, with their averages in different zones ranging from 26.66% to 52.38%. Since properties bought for immediate development should have a premium of zero, our findings in Table 7 seem to suggest that land purchases in the ‘north’, ‘east’ and ‘west’ of Attica are the most ‘speculative’ in nature.3

As previously discussed, the estimates in Table 7 are affected by assumptions regarding a number of needed input parameters. However, since the option and intrinsic values are equally affected by these parameters, we expect our calculations and conclusions to be relatively unaffected by the assumptions made.

Concluding Remarks

The real options approach to capital investment has offered practitioners a number of ground-breaking theoretical research papers that collectively constitute an innovative conceptual framework for analyzing decision-making under uncertainty. However, empirical and applied studies in the area have been few and far between.

This paper contributes to the literature by being the first (to the best of our knowledge) that empirically tests the predictions of a real options model using micro-level, real estate data from a Euro area member country. More specifically, we provide evidence of real options in recent land transaction prices from the Greek real estate market.

We compare land values from a real options model, with the values from a simple discounted cash flow (DCF) approach (that ignores the option to wait to develop). Our results establish the existence of significant “real option premia” in land transaction prices from the Attica prefecture of Greece. These premia are found to be significant in magnitude, with a mean of 36% across all sample observations, and are highest in magnitude for land transactions in the north and west suburbs of Athens, suggesting that land purchases in these areas have been more speculative in nature during the time period under review.

Moreover, we provide estimates of implied standard deviations of individual housing properties in the region of 15 to 21% per annum. These are comparable to-if not slightly lower than-estimates reported in earlier studies, and seem to suggest that idiosyncratic risk levels inherent in recent prices of land in Greece are lower than those reported in other countries.

Footnotes

  1. 1.

    The construction factors represent the number of m2’s that the owner of 1 m2 of land is allowed to develop in a given area. These are determined by the civil planning regulations of the Ministry of Environment, Energy and Climate Change (www.ypeka.gr), and so are the coverage factors, the proportion of the constructed m2’s that are allowed to constitute a built individual property.

  2. 2.

    This point is further analyzed in B. Hedonic Estimation section.

  3. 3.

    It should be noted that Table 7 reports, for each zoning category, the average option value and the average intrinsic value (in euros), and the average real option premium (and not the option premium of the average values).

Notes

Acknowledgements

Thanks are due to an anonymous referee, Steven R. Grenadier (the editor), Athanasios Episcopos, Georgios Leledakis, Leonidas Rompolis, Thodoris Theodorakopoulos from RE/MAX Hellas, G. K. from Aspis Real Estate and Panayiotis Stamatis from Denaro Real Estate, as well as participants at the Empirical Finance session of the 9th HERCMA conference in Athens, Greece and the 2008 international conference on Applied Business and Economics in Thessaloniki, Greece. Usual disclaimers apply.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Accounting & FinanceAthens University of Economics & BusinessAthensGreece
  2. 2.Ace-Hellas SAAthensGreece

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