GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.187

Real Options Valuation of Abandoned Farmland

Michi Nishihara

March 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Real Options Valuation of Abandoned Farmland
Michi NISHIHARA∗

Abstract
I investigate the decision-making process of an owner of abandoned farmland that iscurrently restricted to agricultural use but will be available for nonagricultural use in the
future. I ﬁnd that a slight probability of land conversion greatly increases the land value
and discourages the owner from cultivating the land. I also observe that a small gap in
the anticipation of land conversion prevents the owner from selling or leasing the land toa more eﬃcient farmer.

JEL Classifications Code: G13, Q15, R14.
Keywords: real option, abandoned farmland, land development, land conversion.

∗

The ﬁrst version: 30 March, 2011. Corresponding Author, Address: Graduate School of Economics, Osaka

University, 1-7 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan, E-mail: nishihara@econ.osaka-u.ac.jp,
Tel: 81-6-6850-5277

1Introduction

Recently, there has been increasing concern about whether food production can keep pacewith population growth in the future ([6]). Promoting the eﬀective use of agriculturalland is critical in resolving the issue. However, abandoned farmland that will not be
cultivated for several years has become more prevalent in Japan. In fact, Japan’s total
area of abandoned farmland has almost tripled in the last two decades.
The purpose of this paper is to investigate the problem of abandoned farmland and oﬀer
suggestions for promoting its eﬀective use. I investigate the decision-making process of anowner of abandoned land using the real options framework. The real options approach, inwhich option pricing theory is applied to real investment problems, is useful in evaluating
land development in the face of uncertainty about cash ﬂows from the development ([14, 1,
2, 5]). For instance, [1, 2] apply real options models to land conversion decisions, whereas[5] investigates land development timing with an alternative land use choice in terms ofa max-option. Several papers, including [12, 11, 10], provide empirical evidence for real
options valuations. Although the previous studies assume that the owner optimizes thedevelopment (or conversion) timing, this is not the case with Japan’s abandoned farmland.
In most cases, abandoned farmland is currently restricted to agricultural use but will beavailable for nonagricultural use with environmental and regulatory changes at some pointin the future.
This paper models the decision-making process of an owner of abandoned farmland
as follows. An opportunity that enables development for nonagricultural use comes as an
exponential distribution. Before the arrival of the conversion opportunity, the owner has
the option to cultivate the land with sunk costs at an arbitrary time. As soon as the land
conversion opportunity arrives, the owner will immediately sell the land to a developer
for residential or commercial use. This assumption is consistent with the fact that theprice of land for nonagricultural use is much higher than that of land for agricultural use.
To maintain brevity, I assume that cash ﬂows from agricultural and nonagricultural land
use follow bi-dimensional geometric Brownian motions.
Although the problem is expressed as a complex bi-dimensional optimal stopping problem, I reduce it to a standard one-dimensional problem and derive a closed-form solution
under plausible assumptions. The value of abandoned land is derived as a sum of thevalues of the cultivation option and prospective land conversion. Further, I calibrate themodel with Japan’s land price data from 2005. Results show that a slight probability of
conversion greatly increases the value of abandoned land and discourages the owner from
cultivating the land. I argue that, in order to promote agricultural use of land, the government needs a zoning ordinance that completely removes owners’ anticipation of land
conversion. It seems that owners’ abandonment of farmland is primarily caused by the
insuﬃcient restriction.

1

In addition, I explore why an owner of abandoned farmland neither sell nor lease
the land to a more eﬃcient farmer. With the same anticipation of land conversion, an
ineﬃcient owner would sell or lease the land to a more experienced farmer who is eager tocultivate it. However, in Japan’s current system, less productive farmers are more likely
to receive permission for land conversion. As a result, the anticipation of land conversion
diﬀers between ineﬃcient and eﬃcient farmers. I demonstrate that only a small gap in
the anticipation prevents the owner of abandoned land from selling or leasing the land toa more productive farmer. As a policy implication, I argue that the government needs a
uniﬁed guideline for all farmers, even if it does not completely remove the anticipationof land conversion due to the prospective Trans-Paciﬁc Partnership (TPP) which mightforce the government to deregulate the conversion of agricultural land.

2

Abandoned farmland in Japan

Abandoned farmland is deﬁned as farmland that has been left idle for more than one year
and will not be cultivated for several years. It is ineﬃcient from the perspective of land
use and has negative consequences, such as increasing the prevalence of harmful insects
and the illegal dumping of waste, on the community. Recently, a proliferation in theamount of abandoned farmland has become a serious issue in Japan. Japan’s total areaof abandoned farmland increased from about 130, 000 hectares in 1985 to about 386, 000
hectares in 2005. Typically, owners of abandoned farmland are heirs to their parents’ land.
They have jobs in urban areas and do not intend to cultivate the inherited land. Many
individuals who are engaged in agriculture are aging, which will aggravate the problem ofinheritance. Tax savings and the conversion of agricultural land are major reasons why
owners of abandoned farmland neither sell nor lease their abandoned land. In this paper,
I concentrate on the problem of land conversion. According to [13] who investigates thecase of rice land in Japan, the price of land converted for nonagricultural use is almost
ﬁve times higher than the original price.
In Japan, the Agricultural Land Act controls the conversion of farmland to protect
agricultural land. In principle, owners need to receive permission from the prefectural
governor (or the minister of agriculture in cases involving more than 4 hectares) when they
are ready to covert agricultural land for other use. Agricultural land is classiﬁed into ﬁve
categories which determine the permission guidelines. For the purpose of improving thefood self-suﬃciency rate, almost 90% of farmland is classiﬁed into a category that is zonedby the Prefectural Programs for Establishment of Agricultural Promotion Regions. The
conversion of farmland in this category for nonagricultural use is supposed to be impossible“in principle.” However, the guideline, unlike zoning ordinances in the European Union,
is not executed rigorously. Actually, for some obscure reason, owners are sometimes2permitted to convert farmland in this category for nonagricultural use. For example,
in 2005, 0.31% of rice land was converted for nonagricultural use ([13]). In addition, inJapan’s current system, the possibility of obtaining permission for land conversion is higher
if a farmer is less eﬃcient (e.g., those with small-scale and unproductive farms). This
ambiguous restriction increases owners’ anticipation of converting abandoned farmland
for nonagricultural use.
The TPP is the multilateral free-trade agreement that aims to integrate the economiesof the Asia-Paciﬁc region. The Japanese government is currently facing a diﬃcult decision
regarding whether to join the TPP. Although entry into the TPP is required to maintainthe competence of the Japanese manufacturing industry, the elimination of tariﬀs on
key agricultural products by the TPP has created serious concerns among farmers. The
agriculture ministry claims that the elimination of agricultural tariﬀ greatly increases
the number of imports of cheaper farm products from the Asia-Paciﬁc region, forcing
many small-scale farms to close. Naturally, the conversion of agricultural land will begreatly deregulated if Japan decides to join the TPP. This uncertainty about the TPP
also increases owners’ anticipation of land conversion in the future.

3

Real options valuation

Consider an owner of abandoned farmland. The land is restricted to agricultural use
at the initial time, but an opportunity that enables nonagricultural development arrives
as an exponential distribution (Poisson arrival) with intensity λ. Note that rare events
such as regulatory and environmental changes are usually modeled as Poisson arrivals
in the real options literature (e.g., [7]). Cultivating abandoned land for agricultural use
requires initial investment costs of I1 (> 0), while developing the land for nonagricultural
use requires initial investment costs of I2 (> 0). The land generates risk-adjusted cash
ﬂows X1 (t) by agricultural use and X2 (t) by nonagricultural use. The risk-adjusted cash
ﬂows X(t) = (X1 (t), X2 (t)) are random and follow geometric Brownian motions
dXi (t) = µi Xi (t)dt + σi Xi (t)dBi (t), Xi (0) = xi (> 0)
where B1 (t), B2 (t) are Brownian motions with correlation coeﬃcient ρ. Constants µi
and σi (> 0) denote the risk-adjusted growth rate and volatility, respectively. Mathematically, the model is built on the ﬁltered probability space (Ω, F, P ; Ft ) generated by(B1 (t), B2 (t)). The set Ft represents the set of available information at time t, and theowner optimizes the policy under this information. The risk-free rate is a constant r(> 0).
For convergence, r > µ is assumed. Refer to [4] for the economic rationale for this assumption.

3

3.1

Model solution

This section provides a real options valuation for abandoned farmland. The value ofabandoned (cultivated) farmland that is available for nonagricultural purpose is denotedby F0 (X(t)) (F1 (X(t))) for the state variables X(t). For X(0) = x, the value of abandoned
farmland is expressed as the following optimal stopping problem:
(∫ y
)
∫ ∞
−rt
−rτ
−ry
V (x; λ) := sup E[{1{τ <y}e X1 (t)dt − e I1 + e F1 (X(y))
τ ∈T

0

τ

+1{τ ≥y} e−ry

F0 (X(y))}λe−λy dy],(1)where T denotes the set of all stopping times. In (1), τ means the time of cultivation,
while y means the time when the land permission conversion is provided. At t = y, thevalue of land becomes F0 (X(y)) for y ≤ τ and F1 (X(y)) for y > τ . Formally, F0 (X(t)) is
the value of the option to develop the land for either agricultural or nonagricultural use,
whereas F1 (X(t)) consists of a current cash ﬂow from the cultivated land and the option
value of the nonagricultural development. Both F0 (X(t)) and F1 (X(t)) may include thevalue of the option to switch between agricultural and nonagricultural land use in the
future. It is impossible to derive any closed-form solution to the bi-dimensional problem(1), although several studies, including [3, 8, 9], showed the properties of solutions tomulti-dimensional optimal stopping problems.
As mentioned in the previous section, in reality, the price of land converted for nonagricultural use is almost ﬁve times higher than that of land for agricultural use ([13]). Whenpermitted to convert agricultural land to nonagricultural use, most owners immediately
sell the land to residential or commercial developers. Considering this fact, I assume that

and

x2
x1
− I1 <<− I2
r − µ1r − µ2(2)∫ ∞X2 (t)F0 (X(t)) = F1 (X(t)) = E[e−r(s−t) X2 (s)ds − I2 | Ft ] =− I2 .
r
− µ2
t

(3)

Assumption (3) means that land is developed for nonagricultural use as soon as the land
conversion permission is provided. This is a good approximation of the reality. In addition,by (3) I can reduce problem (1) to a standard one-dimensional optimal stopping problem
and derive a closed-form solution as follows.
Proposition 1
V (x; λ) = V1 (x1 ; λ) + V2 (x2 ; λ),
 (





where
V1 (x1 ; λ) :=






x∗1 (λ)− I1
r + λ − µ1

)(

x1
− I1
r + λ − µ1x1∗x1 (λ))β(0 < x1 < x∗1 (λ))(5)(x1 ≥ x∗1 (λ)),4(4)

β(r + λ − µ1 )I1
β−1
√(
)
1 µ1
µ1 1 2 2(r + λ)−+β := − 2 +
2 σ1
σ12 2
σ12
x∗1 (λ) :=V2 (x2 ; λ) :=

λx2
λI2
−
.
(r − µ2 )(r + λ − µ2 ) r + λ

(6)

(7)

Proof By (3) I can simplify (1) as follows:
V (x; λ)
(∫ y
)
(
)}
∫ ∞{
X2 (y)−ry−rt−rτ
1{τ <y}λe−λy dy]= sup E[e X1 (t)dt − e I1 + e
− I2
r
−
µ
2
τ ∈T
0
τ
)
∫ ∞ (∫ y
λx2
λI2
−rt
−rτ
= sup E[e X1 (t)dt − e I1 λe−λy dy] +−(r − µ2 )(r + λ − µ2 ) r + λ
τ ∈T
τ
τ
(
)
X1 (τ )λx2
λI2
= sup E[e−(r+λ)τ
− I1 ] +
−
.
(8)
r
+
λ
−
µ
(r
−
µ
)(r
+
λ
−
µ
)
r
+λ
1
2
τ ∈T
{z 2
}
|
{z
} |
=V2 (x2 ;λ)=V1 (x1 ;λ) one-dimensional problem

To obtain (8), I used)
∫ ∞ (∫ y−rt−rτE[e X1 (t)dt − e I1 λe−λy dy]ττ)∫ ∞ (∫ y+τ
−rt
−rτ
= E[
e X1 (t)dt − e I1 λe−λ(y+τ ) dy]0τ)∫ ∞ (∫ y+τ
−rte X1 (t)dt λe−λ(y+τ ) dy] − E[e−(r+λ)τ I1 ]
= E[
0

(9)

τ

∫ ∞ −rτe X1 (τ )(1 − e−(r−µ1 )y ) −λ(y+τ )= E[
λedy] − E[e−(r+λ)τ I1 ]r − µ10
X1 (τ )= E[e−(r+λ)τ
] − E[e−(r+λ)τ I1 ],r + λ − µ1(10)where I used the change of variables in (9), while I obtained (10) by the tower property
and the strong Markov property of X1 (t). Note that, in (8), the optimal stopping problem
V1 (x1 ; λ) depends only on X1 (t). This enables us to derive the value function (5) and thethreshold (6) in closed forms (e.g., [4]). The proof is complete.

Proposition 1 shows that the value of abandoned farmland, V (x; λ), is composed of twovalues: the value of the option to cultivate the land, V1 (x1 ; λ), and the value of prospective
land conversion, V2 (x2 ; λ). The owner cultivates the land which is restricted to agricultural
use when the cash ﬂow from farm products, X1 (t), increases above the threshold x∗1 . The
decision on the cultivation timing is independent of the dynamics of the cash ﬂow by
nonagricultural use, X2 (t). When the intensity λ goes to 0, V (x; λ) converges to V1 (x; 0).
On the other hand, when λ goes to ∞, V (x; λ) converges to x2 /(r − µ2 ) − I2 , which is thevalue of the immediate development for nonagricultural use. By (2), (4), and (6) I have∂V (x; λ)/∂λ > 0 and dx∗1 (λ)/dλ > 0.

5

3.2

Model calibration

In the following numerical example, I consider a typical case. The owner has another job
and owns 50 ares of farmland, which has been abandoned for many years. In 2005, theaverage price of 50 ares of rice land was approximately 27 million yen (the exchange rate
average was 1 yen ≈ 0.009 dollars in that year), whereas the average price of land thatwas permitted to convert for nonagricultural use was 130 million yen ([13]). I set theinitial investment cost as I1 = 15 million yen which consists of three parts:
I1E = 5 million yen: Extra costs stemming from abandoned land. Preliminary work, suchas restoring soil, is required to convert abandoned land into farmland.
I1O = 8 million yen: Ordinary initial costs of cultivation. Farming equipment, such as afarm tractor, requires high initial costs.
I1I = 2 million yen: Costs stemming from the owner’s ineﬃciency. The owner is lesseﬃcient than an average farmer because he/she is not accustomed to farming.
Plausible parameter values of r = 0.07, µ1 = 0.03, and σ1 = 0.2 are assumed. To ﬁt
the fact that the average price of farmland was 27 million yen, I set the value of x1 as asolution tox1− I1O = 27.
r − µ1
Therefore, I have x1 = 1.4, which means that the annual income reaches approximately
1.4 million yen from the cultivated farmland. This value is consistent with the average
income from farm products at a small farm. Note that an owner of a small farm frequently
has another job. To ﬁt the fact that the average price of converted land was 130 million
yen, I set
x2− I2 = 130.
r − µ2(11)

However, it is diﬃcult to estimate x2 and I2 individually because they diﬀer across land
uses. To avoid this calibration challenge, I set the plausible parameter value of µ2 = 0.
In this case, I do not need to specify x2 and I2 because by (7) and (11) I have
V2 (x2 ; λ) =)λ ( x2
130λ− I2 =.
r+λ r
0.07 + λFor expositional purposes, I deﬁne p := − log(1 − λ), which denotes the probability
that the land conversion permission will be provided within one year. As mentioned in
Section 2, in 2005, 0.31% of rice land was converted for other use. This percentage is notequal to p because not all farmers applied for land conversion permission. In addition, thepercentage depends greatly on the regions and farm scales. For instance, more than 1%of race land was converted around urban areas, such as Tokyo, Kanagawa, and Osaka. In
this paper, I present the results with varying levels of p from 0 to 0.05(= 5%).
Figure 1 shows the land value V (x; λ), value of the cultivation option, V1 (x1 ; λ), valueof prospective land conversion, V2 (x2 ; λ), and threshold x∗1 (λ). A slight probability of6

land conversion greatly increases V (x; λ) and x∗1 (λ). For example, compared to V (x; λ) =20.1, V1 (x1 ; λ) = 20.1, V2 (x2 ; λ) = 0, and x∗1 (λ) = 1.54 million yen for p = 0, I haveV (x; λ) = 30.2, V1 (x1 ; λ) = 13.95, V2 (x2 ; λ) = 16.25, and x∗1 (λ) = 1.93 million yen for
p = 0.01 = (1%). Only a small probability of land conversion makes V2 (x2 ; λ) higher thanV1 (x1 ; λ). Note that, the nonagricultural value (11) does not inﬂuence x∗1 (λ), although
it inﬂuences V (x; λ). In conclusion, in order to promote agricultural use of land, thegovernment needs a zoning ordinance that completely removes owners’ anticipation of land
conversion. The problem of abandoned farmland primarily arises from Japan’s insuﬃcient
restriction.
Next, I consider why ineﬃcient owners of abandoned land neither sell nor lease theland to farmers who are experienced in managing large farmland. Assume that an eﬃcient
farmer requires an investment cost of I1 := I1E + I1O = 13 million yen, which is lower
than I1 = I1E + I1O + I1I = 15 million yen for the ineﬃcient owner. Figure 2 compares thecases of I1 = 15 and I1 = 13. For I1 = 13, due to the eﬃciency, the land value V (x; λ) ishigher and the cultivation threshold x∗1 (λ) is lower. Then, with the same anticipation ofland conversion, the owner would sell or lease the land to the eﬀective farmer who is moreeager to cultivate the land. However, this is not the case. In Japan’s current system, p ishigher for the ineﬃcient owner than the eﬃcient farmer. As mentioned in Section 2, thepossibility of obtaining land conversion permission is greater for less eﬃcient farmers. In
addition, productive farmers, such as agricultural corporations, rarely attempt to convert
agricultural land for other use. The left panel in Figure 2 shows that, with only a small
gap in p, the land value for the ineﬃcient owner increases far beyond that of the eﬃcient
farmer. This prevents the ineﬃcient owner from selling or leasing the land. Accordingly,
I argue that the government needs a uniﬁed guideline for all farmers, even if it does
not completely remove the inﬂuence of owners’ anticipation of land conversion due touncertainty about the TPP.

Acknowledgments
This work was supported by KAKENHI 22710142.

References[1] D. Capozza and R. Helsley. The stochastic city. Journal of Urban Economics, 28:187–
203, 1990.
[2] D. Capozza and Y. Li. The intensity and timing of investment: The case of land.
American Economic Review, 84:889–904, 1994.

7

4

60

V(x;λ)
V1(x1;λ)3.550V2(x2;λ)3

Threshold

Value

70

40
30
20

2.5
2
1.5

10
0

x∗1(λ)

0

0.01

0.02

0.03

0.04

1

0.05

0

0.01

0.02

p

0.03

0.04

0.05

p

Figure 1: The left panel plots V (x; λ), V1 (x1 ; λ), and V2 (x2 ; λ). The right panel plots x∗1 (λ).

70

4
I1=15
I1=13

50
40
30
20

I1=15

3.5
Threshold

Value

60

I1=13

3
2.5
2
1.5

0

0.01

0.02

0.03

0.04

1

0.05

p

0

0.01

0.02

0.03

0.04

0.05

p

Figure 2: The left panel plots V (x; λ) for I1 = 15 and I1 = 13. The right panel plots x∗1 (λ) for
I1 = 15 and I1 = 13.

8

[3] J. Detemple. American-Style Derivatives valuation and computation. Chapman &Hall/CRC, London, 2006.
[4] A. Dixit and R. Pindyck. Investment Under Uncertainty. Princeton University Press,
Princeton, 1994.
[5] D. Geltner, T. Riddiough, and S. Stojanovic. Insights on the eﬀect of land use
choice: The perpetual option on the best of two underlying assets. Journal of Urban
Economics, 39:20–50, 1996.
[6] B. Gilland. World population and food supply: can food production keep pace withpopulation growth in the next half-century? Food Policy, 27:47–63, 2002.
[7] S. Martzoukos and L. Trigeorgis. Real (investment) options with multiple sources ofrare events. European Journal of Operational Research, 136:696–706, 2002.
[8] M. Nishihara. Hybrid or electric vehicles? a real options perspective. Operations
Research Letters, 38:87–93, 2010.
[9] M. Nishihara. Real options with synergies: static versus dynamic policies. Journalof the Operational Research Society, forthcoming, 2011.
[10] A. Plantinga, R. Lubowski, and R. Stavins. The eﬀects of potential land development
on agricultural land prices. Journal of Urban Economics, 52:561–581, 2002.
[11] A. Plantinga and D. Miller. Agricultural land values and the value of rights to future
land development. Land Economics, 77:56–67, 2002.
[12] L. Quigg. Empirical testing of real option-pricing models. Journal of Finance, 48:621–
640, 1993.
[13] K. Saitoh and H. Ohashi. The eﬀects of prospective conversion of agricultural landon the scale and productivity of rice land. RIETI Discussion Paper Series 08-J-059(in Japanese), 2008.
[14] S. Titman. Urban land prices under uncertainty. American Economic Review, 75:505–
514, 1985.

9