Real Option Analysis as a Tool for Valuing Investments in

May 10, 2011 Draft – For Review Only

Real Option Analysis as a Tool for Valuing Investments in Adaptation to Climate Change

Peter Linquiti and Nicholas Vonortas

The Center for International Science and Technology Policy George Washington University

1. Overview

The challenge of adapting to climate change is a daunting one, particularly for developing

countries. Climate-driven impacts will likely be substantial while investments in adaptation will

be limited by resource constraints and competing demands from other development priorities. In

this analysis, we explore whether a real option paradigm that explicitly recognizes uncertainty

and maintains future flexibility can provide an investment strategy that developing countries

would find beneficial. We use a Monte Carlo model to test the strategy for two coastal cities in

developing countries and find that, under certain circumstances, a real option strategy has the

potential to reduce the costs of adapting to climate change.

2. Introduction

2.1. Global Context

Even if global greenhouse gas (GHG) emissions are reduced in the near future, continued

warming of the climate now appears unavoidable, leading the Intergovernmental Panel on

Climate Change (IPCC) to conclude that at least some adaptation to climate change will be

necessary (IPCC, 2007a). Particularly in low-income countries, decisions about adaptation will

be made in the face of scarce resources and competing social and economic development

priorities (IPCC, 2007d). The difficulty of such decisions will be exacerbated by the high stakes

involved. The World Bank estimates that adaptation to 2!C of warming could cost developing

countries between $70 billion to $100 billion per year by 2050 and that such costs are likely to be

very unevenly distributed across regions (2010). At the same time, the consequences of climate

change will fall heavily on developing countries, not only because of limited resources, but also

because so many are located in low-latitudes, where climate impacts are expected to be more

severe (Mendelsohn, Dinar, & Williams, 2006).

Decisions about how best to adapt to climate change will be made in an environment of

substantial uncertainty. In its latest report, the IPCC noted at least 18 key uncertainties in our


understanding of the causes and effects of climate change (IPCC, 2007c). Global emissions of

greenhouse gases in the coming decades, for example, will be driven by difficult-to-forecast

forces such as the extent of development in countries around the world, the state of the global

macroeconomy, choices among existing and new technologies by consumers and firms, and

policy measures implemented either multilaterally or within specific countries. Similarly, while

scientists are becoming more adept at characterizing the relationship between greenhouse gas

emissions and climate impacts, significant uncertainty remains about the nature, magnitude, and

regional distribution of a broad range of impacts including sea level rise, extreme weather events,

water scarcity, eco-system impacts, and changes in agricultural productivity, disease patterns,

and human migration. Finally, as the impacts of climate change manifest themselves,

individuals, firms, communities, civil society, and governments will make hard-to-predict

choices about how to adapt to changes in the planet’s climate. Made autonomously or as

purposive policy, such choices will reflect available technical options, resources, capabilities,

and competing priorities and likely be driven by a mix of economic, political, and institutional

considerations. In short, when it comes to adaptation to climate change, uncertainty is

significant and pervasive across multiple dimensions.

Current uncertainties notwithstanding, however, our collective scientific understanding of

global climate change and its potential impacts has improved markedly in recent years (National

Research Council, 2010). The IPCC began its series of extensive peer-reviewed assessments of

the relevant scientific literature in 1990. The latest assessment, released in 2007, contains

several instances in which IPCC observes that important uncertainties are being reduced over

time (IPCC, 2007b). For example, the Panel now describes as “unequivocal” the conclusion that

the climate is warming, whereas back in 1990, natural variability could not be ruled out, forcing

the Panel to conclude that the “unequivocal detection of the enhanced greenhouse effect from

observations is not likely for a decade or more” (IPCC, 1990). Similarly, the Panel now

characterizes the relationship between greenhouse gas emissions and observed global

temperature increases as “very likely,” while in 2001, the relationship was characterized simply

as “likely.” Other areas where scientific progress has been made, relative to the 2001

assessment, include:


… large amounts of new and more comprehensive data, more sophisticated analyses of data, improvements in understanding of [climate] processes and their simulation in models, and more extensive exploration of uncertainty ranges (IPCC, 2007b, p. 2).

Given the global resources being devoted to climate change research, it seems reasonable to

assume that progress in reducing scientific and other uncertainties will continue. The IPCC, for

example, recently launched its fifth global assessment of climate change intended to synthesize

the latest scientific literature. It will be completed by 2014 (IPCC, 2010). As a result, our

understanding of important scientific phenomena and of the impacts of localized climate change

is likely to improve. Even if, going forward, scientific research yielded no new insights (a

seemingly unlikely scenario), the simple passage of time would allow for additional direct

observation and measurement of the impacts of climate change.

Today’s policymakers thus face a dilemma. Should they make irreversible investments in

adapting to potential climate change? Or should they take the risk of delaying action until

uncertainty has been reduced and actual climate impacts are being felt? Perhaps there is a

middle course in situations where investments made today create the opportunity, though not the

obligation, to take a future action to adapt to climate change. To resolve this dilemma,

policymakers require a framework for systematically considering the costs and benefits of these

three possibilities.

In our view, the ideal framework for making adaptation decisions in developing countries

would comprise several elements. It would explicitly incorporate uncertainty about the future

conditions that will ultimately determine the value of today’s adaptation investments. It would

also recognize that such uncertainties are likely to diminish over time, thanks to both

improvements in forecasting techniques and the passage of time over which actual climate

impacts can be observed. The decision-making paradigm ought to recognize that many

investments in adapting to climate change are not “now-or-never” investments, but rather that the

flexibility often exists to expand, contract, or otherwise modify such investments. In addition,

the framework should recognize that adaptation investments are rarely “all-or-nothing”

investments, but instead are choices along continua of costs, risks, and benefits. Finally, the

framework ought to recognize that delayed investment in adaptation may create additional risk of

climate-driven damages – now or in the future. We concur with Weyant when he notes that:


Climate change is a long-run problem that will provide us with many opportunities to learn and to revise our strategy over many decades. Thus, it is best conceived of as a problem requiring sequential decision-making under uncertainty rather than requiring a large, one-shot, “bet-the-planet” decision (Weyant, 2008, p. 88).

2.2. Characterizing Investments in Adaptation as Real Options

This paper explores whether a real options paradigm can provide a useful framework for

making policy decisions in such situations. In this section, we begin with a brief explication of

the key concepts underlying real option analysis, move to a quick review of the literature in this

field, and then conclude by framing the research questions that motivate this analysis.

2.2.1. Conceptual Explication

Real options are similar to financial options in that both give the option holder the right, but

not the obligation, to take a future action if doing so is advantageous based on future conditions.

For a financial option, the opportunity for action typically involves a time-limited right to buy or

sell a financial asset such as a share of stock or a commodity contract for a specified price. By

contrast, the term “real options” refers to cases where the underlying asset is a real asset such as

land, natural resources, a business opportunity, valuable information, or enhanced protection

against hazards. Real options exist when future outcomes are uncertain, the uncertainty is likely

to be reduced over time, the flexibility exists to take action in the future as the uncertainty is

resolved, and the action can reduce costs or increase benefits when it is taken (Triantis, 2003).

Real option analysis has been applied in myriad contexts including, among others, corporate

research and development, oil and gas exploration projects, mergers and acquisitions, real estate

development projects, and public sector research and development (Shockley, 2007), (Triantis,

2001), (Vonortas & Desai, 2007).

If a real option exists but is not properly valued, the traditional decision criterion of

maximizing net present value may yield a suboptimal choice (Copeland & Antikarov, 2003),

(Shockley, 2007), (Triantis, 2003). In the typical cost-benefit analysis, uncertainty is captured

through the use of expected values which reflect the mean values of the stochastic distributions

that describe the relevant uncertainties. The effect of this approach is to attach a “now-or-never”

quality to the investment choices; this quality is appropriate if indeed no flexibility exists to

adjust today’s decision in future time periods. If, on the other hand, decision-makers can adjust


the investment in the future (e.g., expand, contract, or abandon it), then the standard net present

value framework will tend to under-value this flexibility.

In characterizing the potential contribution of real option analysis to the proper valuation of

investments under uncertainty, it is helpful to distinguish the process of framing options from the

process of valuing them. In many cases, simply framing a decision as a choice among

alternatives, some of which entail options, can go a long way toward improving the quality of the

decision. Decision trees are often used to map out complex option-based investments by

defining sequential decisions to be made over time, as new information becomes available and

uncertainty is reduced. Corporate users of real option techniques across industries in the U.S.

report that, beyond putting a number to an investment choice, option analysis represents a way of

thinking that allows entire organizations to be more rigorous in their characterization of potential

business opportunities (Triantis, 2001).

When it comes to option valuation, a quick look at a modern finance textbook reveals that

there exists a large body of relevant literature, dating back to the development of the Black-

Scholes-Merton (BSM) model in the early 1970s (Hull, 2009). In addition to the BSM model,

other popular valuation techniques include binomial option pricing, risk-adjusted decision trees,

and Monte Carlo analysis (Triantis, 2003). The restrictive assumptions of the BSM model often

cannot be met when valuing real options, so one of the other three techniques is typically used.

Several parameters drive the value of an option – real or financial – including the present value

of the underlying asset, the uncertainty of that present value, the time interval from the initial

decision to the subsequent decision, the cost that would be incurred at the subsequent decision

point, and the discount rate (Copeland & Antikarov, 2003).

There are a number of potential investments in adaptation to climate change that have option-

like characteristics. For example, research and development of new cultivars that would be

suitable to a changed climate can create an option for the agriculture sector in a vulnerable

country. If the climate changes as expected, the new cultivars can be quickly deployed (i.e., the

option would exercised). If the climate remains relatively unchanged, then the new cultivars

would not be used (i.e., the option would be allowed to expire worthless). In this case, the R&D

cost can be viewed as the purchase price of the option and the cost to deploy the new cultivars

would be the exercise price. Similarly, a firm operating in a vulnerable coastal zone might buy


property at a higher elevation. If significant sea level rise occurs, the vacant land would give the

firm the option (though not the obligation) to relocate its operations out of harm’s way. The cost

of the land would be the purchase price of the option and the cost of relocation would be the

exercise price.

2.2.2. Prior Literature

There exists a small body of literature that links real option analysis to investments in

adaption to climate change.1

Despite these early efforts, however, the potential application of real option analysis to

adaptation projects appears to have received only limited attention from key policymakers

responsible for the United Nations Framework Convention on Climate Change (UNFCCC). For

example, in preparation for the 16th Conference of the Parties to the UNFCC in late 2010, one of

the Convention’s subsidiary bodies issued its analysis of how best to analyze the cost and

benefits of adaption investments. The report makes a passing reference to the suggestion of

some participants that real option techniques be used to better characterize uncertainty. This

Guidance issued by the national government in the United

Kingdom, for example, suggests that option analysis be used to appraise adaptation projects that

entail “uncertainty, flexibility and learning potential” (H.M. Treasury, 2009). The U.K. guidance

document includes a case study of a real option analysis of potential flooding in the Thames

Estuary in the coming century. The Environment Department at the World Bank has also noted

the potential relevance of the real option framework to adaption projects and, in a 2009 Guidance

Note, describes the application of the framework to an irrigation project in Mexico (World Bank,

2009). In its Synthesis Report on the Economics of Adaptation to Climate Change, the Bank

also makes a brief reference to real options as a “practical approach” for addressing uncertainty

in investments in adaptation (2010, p. 100). Real option analysis has been applied to adaptation

to climate change in the rain-fed agriculture sector in Yemen (Scandizzo, 2010), in the

residential housing sector in the Mekong Delta of Viet Nam (Dobbes, 2010), in the agriculture

sector in Australia (Hertzler, 2007), and in flood management strategies for the Thames Estuary

(Woodward, Gouldby, Kapelan, Khu, & Townend, 2010).

1 There also exists a literature, not reviewed here, that addresses real option analysis of measures to mitigate climate change.


suggestion did not, however, find its way into the set of recommendations put forth to the Parties

(Subsidiary Body for Scientific and Technological Advice, 2010).

2.2.3. Research Question

In this context, we define our core research question as follows: To what extent would

framing adaptation investments as real options lead to better use of scarce resources in

developing countries? We take as given a policymaker whose objective is cost minimization.

We ignore the prospect of significant benefits from climate change and consider two types of

costs. The first is investments – both capital and recurring – in adaptation measures and the

second is the value of the economic damages that result from climate change despite those

investments in adaption (i.e., residual damages). We assume that policymakers are interested in

these impacts over time and hence seek to minimize the cost of adaptation investments, A,

! = "#$ + %$ + &('$)(1 + ()$

)

$=1

where n is the period over which the investment is analyzed, Ci is the capital expenditure in year

i, Oi is the operation and maintenance cost in year i, E(Di) is the expected value of the residual

damages that occur in year i, and r is the discount rate. In turn, if a particular decision-making

strategy can be shown to lower these costs (i.e., minimize A), we would argue that it offers

policymakers the opportunity to make better use of the resources available for adaptation to

climate change.

We assume that policymakers are risk-neutral when solving this minimization problem,

meaning that they attach the same utility to each “dollar” considered in their analysis. Planners

would thus treat as equivalent a dollar spent with certainty on the cost of a capital investment and

a dollar spent in the form of an increase in the expected value of future damage anticipated to

result from climate change. We thus use a notionally risk-free rate of 3% for r.

Our approach here is consistent with the general principle that government policymakers,

investing on behalf of large numbers of taxpayers across multiple diverse projects throughout the

economy, ought to be risk-neutral (Arrow & Lind, 1970). Two caveats, however, must be kept

in mind. First, as a practical matter, if planners in developing countries do in fact display risk

aversion when making decisions about adapting to climate change, then any simulation of their


behavior needs to reflect such considerations, irrespective of the conclusions of the academic

literature. Second, even in the literature, concerns about the routine application of risk-neutrality

to public decisions have been identified. For a general overview of such concerns, see

Boardman et al. (2006). Particularly relevant here is Weyant’s observation that “there may need

to be some premium [added to the discount rate] to reflect that climate change is a big enough

potential problem to make even whole economies risk averse” (2008, p. 90). We anticipate

returning to the issue of risk-neutrality in future work.

We also recognize that many of the potential impacts of climate change – forced migration,

changes in disease patterns, poverty, loss of life, social disruption – defy easy monetization.

Accordingly, the calculation of the expected value of residual damages from climate change has

both a qualitative and a quantitative component. In order to skirt this issue in our analysis below,

we confine ourselves to two non-economic impacts – loss of life and population displacement –

and attach a monetary value to both, solely for the purposes of more clearly illustrating our

proposed methodology.

In this analysis, we test the potential value of a real option framework for the specific case of

adapting to sea level rise. We chose sea level rise as our focus for several reasons. First, there is

substantial uncertainty about the rate and ultimate magnitude of sea level rise (IPCC, 2007b),

(Lowe & Gregory, 2010), (Rahmstorf, 2010). Second, storm surges are typically recognized as

the event during which rising seas are most dangerous; such surges – even in the absence of

climate change – have historically exhibited substantial variability. Third, from a cost-benefit

perspective, the assets to be protected from sea level rise – economic resources and vulnerable

populations – are not static, but evolve over time, thereby introducing a dynamic element into the

calculation of potential damages. All of these uncertainties combine to make adaptation to sea

level rise a phenomenon particularly well suited to real option analysis.

Consider, for example, Figure 1 which frames coastal planning as a one-off decision where

the height of the flood defense is selected once at the outset of the planning period. Though a

simplified example that portrays continuous variables (sea level rise and the value of vulnerable

assets) as discrete, this decision tree illustrates the dilemma faced by coastal planners: a

traditional case of decision-making under uncertainty. Insufficient protection may lead to

inundation while excessive protection may lead to wasted resources. In addition, the more


Figure 1 Applying “One-Off” Decision Making to Coastal Defense Planning

Chose Height of Defense In Year 1

High

High SLRHigh Asset Value Protected

Low Asset Value Protected

Low SLRHigh Asset Value Over‐

Protected

Low Asset Value Over‐Protected

Low

High SLRHigh Asset Value Inundation:

High Loss

Low Asset Value Inundation: Low Loss

Low SLRHigh Asset Value Protected

Low Asset Value Protected

None

High SLRHigh Asset Value Inundation:

High Loss


Low SLRHigh Asset Value Inundation:

High Loss


Investment Decision Uncertainties Outcome


valuable the vulnerable assets, a parameter that may change over time, the more beneficial are

investments in protection. Framed this way, the rational approach for a risk-neutral decision-

maker is to assess the probabilities of future events and then select the coastal defense with the

lowest expected value cost. As an alternative, Figure 2 re-frames the decision problem as a real

option in which multiple decisions are made over time as uncertainty is resolved and more

knowledge becomes available about both sea level rise and the value of vulnerable assets and

populations. The contrast between Figures 1 and 2 demonstrates why planning for sea level rise

might be enhanced by application of a real option paradigm.

Figure 2 Applying Sequential Decision Making to Coastal Defense Planning

Year 1: Select Height of Defense

Year 1+x: Decide

whether to Raise Defense

Year 1+2x: Decide


Year 1+3x: Decide


Year 1+4x: Decide


Ongoing Reduction in Uncertainty About Sea Level Rise & Value of Vulnerable Assets

X = Number of years between periodic planning decisions.

In addition, from a practical perspective, sea level rise is a substantial threat to developing

countries, as evidenced by a recent World Bank review of global vulnerability to sea level rise

which identified “very heavy potential losses that are much more concentrated in some regions

and countries than others” and a “concentration of highly vulnerable large cities at the low end of

the international income distribution” (Dasgupta, Laplante, Murray, & Wheeler, 2009). More

specifically, an estimated 11 million people live in port cities in low income countries that are

threatened by coastal flooding (Nicholls, et al., 2008). Of course, the threat to coastal areas does

not originate solely in climate-induced sea level rise; other drivers include development patterns

that put populations and economic assets in harm’s way, local land subsidence, inadequate

warning systems, failure to invest in sufficient protection measures, and natural (non-climate-

induced) variability in sea levels and storms. Two well-known examples make the point: the


catastrophic flood in Galveston, Texas in 1900 and the equally catastrophic North Sea Flood of

1953, neither of which presumably was materially influenced by climate change.

Rigorous economic frameworks for planning coastal defenses appear to have emerged in the

Netherlands in the late 1950s (Hillen, Jonkman, Kanning, Kok, Geldenhuys, & Stive, 2010).

Van Dantzig first identified the management decision as a cost minimization problem where the

lower risks created by enhanced protection must be balanced against the increased costs

associated with such protection. While van Dantzig’s framework envisioned a single decision at

one point in time (and thus did not comprise a real option framework), Eijgenraam extended the

framework in 2006 to consider periodic improvements in coastal defenses in response to ongoing

economic development and changes in sea levels. Such a paradigm is conceptually consistent

with the real option approach we take in this study.

3. Methodology

In order to assess the potential value of learning and flexibility under conditions of climate-

induced uncertainty, we compare various strategies that a policymaker might pursue in planning

for coastal defense of a city threatened by rising sea levels. We do so using a Monte Carlo

simulation model that provides a simplified representation of the physical, economic, and

decision-making processes likely to drive the results of these strategies. A key advantage of a

Monte Carlo approach is that, unlike many option valuation methods, it can accommodate

multiple sources of uncertainty and does not require that such uncertainties fit any particular

statistical distribution (Triantis, 2003).

We use the model to analyze two cities, one in a riverine delta area (Dhaka, Bangladesh) and

the other on an ocean coast (Dar-es-Salaam, Tanzania). While the data used in the model are

loosely based on these cities, readers are cautioned that a number of analytic simplifications and

data imputations mean that our results should not be seen as identifying a recommended course

of action for either city. Instead, our analysis is meant to evaluate the relative merits of

alternative investment strategies for dealing with the uncertainties of climate change.

3.1. Strategies Analyzed

We analyzed three investment strategies for constructing coastal defenses. To set a baseline,

however, we first examined a no-action scenario under which policymakers make no investments


in defending against rising sea levels. In this baseline scenario, inundation and its consequences

are driven solely by natural processes, unimpeded by policy intervention. In contrast, each of the

three strategies contemplates at least some investment in coastal protection. Like Figure 1, the

first strategy is an inflexible one, and hence, not a real option. It assumes a single decision –

made as part of a planning process for a 100-year time frame – about the optimal height of the

coastal defense structure. The other two strategies create options by permitting policymakers the

flexibility to increase the height of the defense at multiple points during the 100-year period. In

the first of the real option approaches, which we call the “Sense & Respond” strategy, planners

would rely on local observational evidence about changing conditions and increase the defense

height based on that evidence. Similar to Figure 2, in the second real option strategy, which we

term the “Predict & Respond” approach, planners are assumed to periodically examine current

and predicted conditions over the time left in the 100-year planning horizon to decide whether to

raise the height of the coastal defense. Each of the three strategies, and the method by which it is

operationalized in the analysis, is described in more detail below.

3.1.1. Inflexible Strategy

Under the inflexible strategy, policymakers make a single decision at the start of the 100-year

analysis period. In doing so, they select the height of the coastal defense based on an

optimization strategy intended to minimize the present value of the sum of the protection costs

and the expected value of the residual damages that occur despite the presence of the protection.

Planners are assumed to choose a protection height ranging from 0 to 10 meters, in one-meter

increments. Protection costs are assumed to be known with certainty while planners estimate the

expected value of the residual damages based on the best available information about the rate of

global sea level, the incidence and magnitude of storm surges that threaten the vulnerable city,

and the evolution of economic assets and exposed populations on the land-side of coastal

defenses. For purposes of this analysis, decision-makers are assumed to value an avoided fatality

at $0.163 million in Dar-es-Salaam and at $0.170 in Dhaka.2

2 Unless otherwise noted, all monetary values used in this analysis are expressed in real terms, as 2009 US$.

These values reflect Miller’s

review of 68 studies of the value of statistical life (VSL) conducted across 13 countries and his

finding that the typical value is about 120 times per capita GDP (Miller, 2000). Per capita GDP

in Tanzania is $1,362 (purchasing power parity basis) and is $1,416 in Bangladesh (World Bank


Databank, 2011). We are not aware of estimates of the value of a displaced person in developing

countries; hence, we simply assume the value to be 2.5% of VSL. We are not suggesting that

these values would or should be applied during such analyses; rather, we use these illustrative

values only to capture the high likelihood that planners will consider more than just the size of

the vulnerable economic assets in planning for coastal defense.

Under the inflexible strategy, planners are assumed to estimate for each possible height of the

coastal defense structure, the investment costs and the expected value of the damages for each

year in the 100-year analysis period. The option with lowest net present value (at a 3 percent

discount rate) is then selected. It is possible that planners would chose not to construct any

coastal defenses if doing so were the cost-minimizing choice.

The simulation model then determines the consequences of the planners’ decision. Because

of the stochastic nature of the model (and, more importantly, of future climate conditions), actual

events – sea conditions, vulnerable assets and populations, and the extent of inundation – are

likely to vary from the assumptions made by planners in each iteration of the model. Hence,

costs and damages actually simulated over the 100-year period need not (and typically would

not) match the planning assumptions made by decision-makers in the first year of the model

simulation.

3.1.2. Real Option: Sense & Respond Strategy

The Sense & Respond strategy gives local planners the option of raising the height of the

coastal defense in any year during the 100-year analysis. They are assumed to continuously

observe maximum sea levels in relation to the height of the existing coastal defenses. Such

observations, rather than predictions about future sea levels, are assumed to drive ongoing

decisions about whether to raise the height of the defenses. More specifically, this strategy

assumes that if the maximum sea level observed over the course of one year exceeds a specified

percentage (in this case, 75%) of the height of the existing defense, the defense is raised in the

subsequent year. The incremental increase in height is assumed to be the higher of 0.5 meters

and 150% of the observed maximum sea in the prior year. Under this scenario, planners may

raise the height of the coastal defense several times over the 100-year analysis (or they may

never raise the height, in the event that observed sea levels never increase enough to trigger

construction of additional defenses).


3.1.3. Real Option: Predict & Respond Strategy

The Predict & Respond strategy is similar to the Inflexible Strategy in that it endeavors to

minimize the sum of the protection costs and the expected value of the residual damages, with

population impacts monetized as before. It differs, however, in that the minimization analysis is

done periodically throughout the 100-year analysis period (in this case, once every 20 years),

rather just once. Planners thus have the option, but not the obligation, to raise the protection

height in years 1, 21, 41, 61, and 81. Unlike the Sense & Respond strategy, this strategy is a

forward looking one. The planning decision is based on extrapolations from observed changes

that have already occurred in sea conditions, vulnerable assets, and vulnerable populations that

are used to predict the conditions expected to occur over the next twenty-year interval. For

example, the decision made in Year 40 would rely on 40 years of observed data to project

conditions for Years 41 to 60. As with the Inflexible Strategy, planners have no assurance that

their predictions of future conditions will prove accurate; however, in this case, planners are

predicting only 20 years, rather than 100 years, into the future. What’s more, these sequential

decisions made over time reflect an increasing quantity of information about how sea levels,

populations, and assets are changing.

3.2. Model

The model is implemented as an Excel spreadsheet, using Oracle’s Crystal Ball add-in to

execute the Monte Carlo analysis. For this study, the model was run for 10,000 iterations, with

each iteration comprising an analysis of the full 100-year planning period. The model is built on

a simplified representation of the process of defending a coastal city against rising seas. Figure 3

provides a graphic representation of how we have conceptualized the process using a standard

risk assessment paradigm that moves from the source of the risk to the ultimate impacts, along

with potential policy interventions in the form of adaptation to climate change.

The simulation model comprises five basic components. First, the height of existing coastal

defenses in each year – which can vary as a consequence of the policy strategy being analyzed –

is simulated. Second, the maximum storm surge is simulated for each year and compared to the

height of the existing coastal defense to determine whether any inundation occurs. Third, in the

event that inundation is simulated to occur, impacts on economic assets and vulnerable

populations are calculated. Fourth, the size of populations and economic assets vulnerable to


Figure 3 Framework for Assessing Adaptation to Sea Level Rise

differing levels of potential inundation is simulated annually, along with changes brought about

by population and economic growth. Fifth, after these processes have been simulated for 100

years within single model iteration, key outputs are recorded and the model moves to the next

iteration, until all 10,000 iterations have been completed. Each of these five model components

is described in more detail below. Figure 4 depicts the simulation of the Sense & Respond

Strategy while Figure 5 depicts the Do-Nothing Baseline, and the Inflexible and Predict &

Respond Strategies.

3.2.1. Simulation of Coastal Defenses

The concept of “coastal defenses” is used in our model to describe a generic barrier – a

seawall or dike – of a certain height that is capable of restraining storm surges below that height

and preventing any inundation of assets on the land-side of that defense. The prospect of a

failure of the barrier is not considered; inundation is assumed to occur only if the barrier is over-

topped by the sea. While this is a simplification, we believe it is a reasonable one, particularly

since our model does include costs for the ongoing annual maintenance and upkeep of the coastal

defense.

The height of the coastal defense, as well as all references to sea levels and storm surges, are

expressed relative to the mean local, astronomically-predicted, high tide level over the course of

the year prior to the start of the 100-year simulation. The model includes the height of both

freeboard and constructed defenses. The former refers to the vertical distance between the water

level and the lowest level at which vulnerable assets or populations exist. One can think of

freeboard – as we use that term here – as the protection afforded by natural beaches, bluffs,


Figure 4 Simulation of Sense & Respond Strategy

Initialize Policy and Technical Variables

Invest in protection in Year 0?

Increment PH0

Yes

No

Initiate Simulationi = Years 1 to 100

Simulate Sea Level SLi = SLi‐1 + GSLRi +

LSLRi

Simulate Worst Storm Surge of

Year I (Si)

“Non‐Event”[SLi+Si ]/[PHi+FB0]<T

“Close Call”T*+SLi+Si ]/[PHi+FB0] *1.0

“Over‐Top”[SLi+Si]/[PHi+FB0] >1.0

Incur O&MYes

Reached Year 100?

Compute & Report Outputs

Update Variables for Next Year

•Vulnerable Population•Vulnerable Assets•Protection Height

Compare [SLi + Si]to [PHi+ FB0]

Qi=SLi+Si‐PHi‐FB0

No

Invest in Defense: Raise PH by max(0.5, [1+SF] * [SLi+Si]); Incur Cost to Build

Value Damage as D=f (Qi, Vi, Popi, EE)

Decrement V & Pop

Recovery: Asset Investment = ReInv% * Remaining Assets; Pop Return = RePop% * Displaced Persons

PH: Built Protection

Height

FB: Natural Freeboard

SL: Sea Level

SLR: Sea Level Rise

GSLR: Global SLR

LSLR: Local SLR

S: Max Annual Surge

T: Action Threshold

SF: Safety Factor

Q: Inundation quantity

VLife: Value of fatality

VDP: Value of

displaced person

V: Vulnerable econ‐

omic assets

Pop: Vulnerable

population

EE: Evacuation

Efficiency

ReInv%: % of lost

assets reinvested after

inundation

RePop%: % of

displaced persons

who return after

inundation


Figure 5 Simulation of Do-Nothing Baseline and Inflexible and Predict & Respond Strategies

Initialize Policy and Technical Variables

Invest in protection in Year 0?

Increment PH0

Yes

No

Initiate Simulationi = Years 1 to 100

Simulate Sea Level SLi = SLi‐1 + GSLRi +

LSLRi

Simulate Worst Storm Surge of

Year I (Si)

“No Inundation”[SLi+Si ]/[PHi+FB0] *1.0

“Over‐Top”[SLi+Si]/[PHi+FB0] >1.0

Incur O&M

Yes

Reached Year 100?

Compute & Report Outputs

Update Variables for Next Year

•Vulnerable Population•Vulnerable Assets•Protection Height*

Compare [SLi + Si]to [PHi + FB0]

Qi=SLi+Si‐PHi‐FB0

No

Value Damage as D=f (Qi, Vi, Popi, EE)

Decrement V & Pop

Recovery: Asset Investment = ReInv% * Remaining Assets; Pop Return = RePop% * Displaced Persons

PH: Built Protection

Height

FB: Natural

Freeboard

SL: Sea Level

SLR: Sea Level Rise

GSLR: Global SLR

LSLR: Local SLR

S: Max Annual Surge

T: Action Threshold

Q: Inundation

quantity

V: Vulnerable econ‐

omic assets

Pop: Vulnerable

population

EE: Evacuation

Efficiency

ReInv%: % of lost

assets reinvested after

inundation

RePop%: % of

displaced persons

who return after

inundation

i=1, 21, 41, 61, 81?*!

No

Decide whether to increase PH*

Yes

* For the Do‐Nothing Baseline, this step is omitted.! For the Inflexible Strategy, this step occurs only in Year 1 (i=1).


and rocky shorelines. The base of the constructed defense is assumed to match the top of the

freeboard; hence, the total protection height is the sum of the freeboard and the defense height.

Our approach to estimating the costs of coastal defense is based on Yohe et al., who decided

after a review of eight studies to use a unit cost of US$750 per linear foot (1990$) for a 1-meter

high sea defense, and that cost rises as the square of the height (Yohe, Neumann, & Marshall,

1999). We inflated the unit cost from 1990 to 2009, using the U.S. Department of Commerce’s

GDP deflator for fixed investments in nonresidential structures (U.S. Council of Economic

Advisors, 2011). Thus, the model estimates the capital cost (K) of the coastal defense as a

function of its height, as follows:

K = $5,617 * [Hn2 – He

2] * L

where Hn is the height of the new structure in meters and He is the height of the existing

structure, if any. L is the length, also in meters, of the coastal defense. Owing to the trapezoidal

shape of the typical defense structure, capital cost rises exponentially with height. The same

algorithm is used to estimate the cost of raising an existing defense as well as constructing a new

structure; in the latter case, the He term is set to zero. Like Yohe et al, we assume annual

maintenance costs for the defense structure equal 4 percent of the historical capital investment.

A similar approach was applied by Ng and Mendelsohn to their analysis of coastal protection in

Singapore (2005).

Visual inspection of the relevant maps led us to assume a length of 75,000 meters for the

length of the coastal defenses in Dar-es-Salaam and 66,000 meters for Dhaka. Based on the

DIVA model, we assumed that the existing height of the protection is 1.5 meters in Dar-es-

Salaam and 3.0 meters in Dhaka (Valfedis, et al.). In both cases, this height was split equally

between naturally occurring freeboard and constructed coastal defenses.

3.2.2. Simulation of Annual Maximum Sea Levels

The maximum simulated sea level in any given year is a function of three variables, one of

which is treated deterministically while the other two are simulated on a stochastic basis. The

first, local sea level rise (LSLR), is simulated to occur at a constant rate each year, irrespective of

ocean conditions. LSLR captures the net effects of changes in location-specific land elevations,

which may increase due to forces such as geologic uplift or decrease due to forces such as


subsidence. In the case Dar-es-Salaam, local sea level rise is assumed to be -1.58 mm per year,

i.e. that local land elevation is increasing (Kebede & Nicholls, 2011). For Dhaka, we assumed

that the historical subsidence rate of 0.65mm per year reported by Milliman and Haq was a

reasonable proxy for future subsidence (1996).

Global sea level rise (GSLR) is treated stochastically, using a two-step process. At the start

of each iteration, the model first selects a single value for the entire 100-year analysis period to

represent the underlying trend in average annual changes in sea levels. This value is drawn from

a normal distribution with a mean of 3mm per year and a standard deviation of 2mm. Then, to

capture annual variability and the “noisiness” of the climate signal, the actual GSLR in any given

year is drawn from a uniform distribution with a mean equal to the simulated underlying trend

for that iteration and a range that extends plus or minus 50 percent around the mean. This annual

simulation assumes independence of each year from all other years; there is no serial correlation.

The third element in the annual calculation of the maximum sea level is an extreme value

distribution that captures variability in storm surges experienced each year. Information on sea

surges for the two studied cities was graciously provided to us by Robert Nicholls of the

University of Southampton who, with colleagues, studied the vulnerability of port cities around

the world to sea level rise (Nicholls, et al., 2008). Information was provided, as of 1995, on the

surge height associated with four annual recurrence intervals (ARI): 1-, 10-, 100-, and 1000-year

events. The ARI represents expected value of the time interval between surge events that exceed

a given level. Because such events are assumed to be statistically independent, it is possible to

have a 100-year event more than once every 100 years. For purposes of stochastic simulation, it

was necessary to convert the ARIs to Annual Exceedance Probabilities (AEPs). We used the

approach specified by the Australian Government’s Bureau of Meteorology (2011) in which:

!&, = 1- .-1!/0

We also updated the 1995 surge heights for 15 years of global sea level rise which we assumed

to equal 3mm per year, as well as for 15 years of local sea level rise which, as described above,

differs between the two cities. We next took the four point estimates of sea heights (and the

associated AEPs) and matched them to a Gumbel maximum extreme value distribution of the

following form:


1(2) = 13 4 .2-53 4 .-.

-(2-5 )3

where ! is the scale parameter and " is the location parameter. The Gumbel distribution is often

used to characterize flooding events (Kotz & Nadarajah, 2000). Table 1 displays selected values

from the extreme value distribution used in this analysis, along with the values of !#$%&#".

Table 1 Extreme Value Distribution for Storm Surges

Annual Exceedance Probability

Annual Return Interval (years)

Annual Maximum Sea (meters)

Dar-es-Salaam Dhaka

0.001 1000 3.30 5.21 0.002 500 3.25 5.06 0.004 250 3.19 4.90 0.010 100 3.12 4.70 0.020 50 3.06 4.54 0.039 25 3.01 4.38 0.095 10 2.94 4.19 0.181 5 2.88 4.02 0.393 2 2.81 3.82 0.632 1 2.75 3.66 !"#$%&'#(#)%*%(&+,- 0.080 0.225 ./"#*0/1&'#(#)%*%(&+2- 2.752 3.661

Some scientists argue that climate change may affect the frequency and intensity of storm events,

but we have not endeavored to capture such a phenomenon in our analysis; instead, the

parameters underlying the extreme value distribution are assumed to be stationary for the full

100-year analysis period.

To simulate the maximum sea in any given year, our model integrates these three variables as

follows. First, the cumulative sea level rise to date is computed as the combination of the

deterministic LSLR and the stochastic GSLR observed in previous years. Second, the maximum

sea surge for the year being analyzed is then simulated and added to the cumulative sea level to

yield the maximum sea level to which the coastal defense is exposed. If this level is less than or

equal to the height of the coastal defense (plus the freeboard), no inundation occurs and the

model moves to simulation of the next year. If the maximum sea level exceeds the height of the

defense, then at least some inundation is simulated to occur.


3.2.3. Simulation of Inundation Events

The extent of inundation depends on the degree to which the maximum sea level exceeds, or

over-tops, the protection height. For example, if the maximum sea is 3.2 meters and the

protection is 2.0 meters, then the difference of 1.2 meters is used to determine the extent of

inundation. The terrain of the vulnerable city is segmented based on its susceptibility to

inundation. The first segment comprises all land area susceptible to flooding in the event of an

over-topping of coastal defenses of 0.5 meters; the second segment comprises lands susceptible

to inundation from an over-topping of 1.0 meters. This framework continues in half-meter

increments, up to the tenth segment which comprises the land area vulnerable to flooding from a

vertical over-topping of 5.0 meters. Continuing the previous example in which the sea over-tops

the protection by 1.2 meters, the model would assume complete inundation of area of the first

and second segments and partial inundation of the area of third segment. Partial inundation is

simulated using linear interpolation; 40 percent of the third segment would be simulated as

flooded because 1.2 is 40 percent of the difference between 1.0 and 1.5 (i.e., the bounds of the

third segment).

The value of the economic assets and size of the human population located within the area of

each of the ten segments in the first year of the simulation is a model input. Again, we are

grateful to Dr. Nicholls for providing the population data for Dar-es-Salaam and Dhaka

(Nicholls, et al., 2008). The data provided were in 1-meter increments; to create the ½-meter

values, we used simple linear interpolation. The data also were for populations as of 2005; we

increased each population estimate to 2009 using the World Bank’s city growth rates (World

Bank Databank, 2011). To estimate asset values within each vulnerable area, we used an

approach sometimes applied by the insurance industry in which assets are estimated at five times

per capita GDP (Kebede & Nicholls, 2011). Table 2 presents the data used by the model.

If a segment in the city is flood by a sea level in excess of the coastal defense, all of the

assets in that segment are assumed to be destroyed, with an asset loss equal to their current

market value. Population impacts are tempered by the prospect of evacuation prior to the

flooding. We assume in our analysis that 75 percent of the population is evacuated and become

“Displaced Persons” as a consequence of the flood; the remaining 25 percent are counted as

fatalities.


Table 2 Vulnerability as a Function of Vertical Quantity (Q) of Over-Topping of Defenses

(First Year of Analysis)

Segment 1 2 3 4 5 6 7 8 9 10

Q (meters) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Dar-es-Salaam

Value of Assets ($m)

125 134 152 169 224 278 374 469 652 835

Population (thousands)

18 20 22 25 33 41 55 69 96 123

Dhaka

Value of Assets ($m)

337 1,153 1,358 1,564 1,770 1,975 2,786 3,598 5,873 8,149

Population (thousands)

48 163 192 221 250 279 393 508 829 1,151

3.2.4. Simulation of Changes in Vulnerability

The size of the populations and assets at risk of inundation do not remain constant in the

model. Instead, they are assumed to vary stochastically over time. The model allows

populations and assets to change at different rates and does so in a stochastic manner. While the

annual average growth rate remains constant over the 100-year analysis period of a single model

iteration, it is initially selected stochastically. Population growth projections were based on data

from the U.N. Population Division (2008). For simulation purposes, we assumed a simple

triangular distribution with a minimum equal to the U.N.’s low estimate, a peak equal to the

medium estimate, and a maximum equal to the high estimate. The U.N.’s projections cover the

period from 2010 to 2050. We assume the same rate will hold for the future, as well. Table 3

provides the population growth used for the simulation, along with the imputed mean of the

distribution.

Table 3 Annual Population Growth Rate Distributions

(Triangular) Dar-es-Salaam Dhaka

Minimum 1.910% 0.360% Peak 2.240% 0.760%

Maximum 2.560% 1.140% Implied Mean 2.237% 0.753%


We could not readily identify a credible source for projecting asset growth over the full 100-

year analytic timeframe. Consequently, we simply assume that asset values will grow at an

average of 4% per year, with a standard deviation of 2%. What’s more, we assume that

population and asset growth are co-vary with a correlation coefficient equal to 0.75. To more

accurately capture year-over-year fluctuations in the rates of change, the actual changes in

populations and assets in any given year are drawn from a uniform distribution with a mean

equal to the simulated underlying trend for that iteration and a range that extends plus or minus

50 percent around the mean.

In the year of an inundation, these population and asset growth rates are not applied. Instead,

the process of asset destruction and population displacement determines the assets and

population that remain at the end of that year. Then, in the following year, the model simulates

re-investment and re-population within the city at rates of, respectively, 25 and 50 percent of the

pre-inundation levels. In the event that a segment has been fully inundated, no re-population or

re-investment is simulated in that segment; instead, asset and population growth is directed to

segments that have not been inundated. Two years after inundation, the process of annual

growth described above resumes, though from the lower, post-inundation levels.

3.2.5. Compilation of Results

The no-action baseline and the three alternative investment strategies are simulated

simultaneously within each iteration of the model to ensure that sea levels, along with the

potential size of vulnerable assets and populations, remain constant as each policy choice is

assessed. (Across iterations, of course, the values of these variables are allowed to vary

stochastically.) For each year, the model records the capital and O&M spending on coastal

defenses, whether the protection height has been raised under the Predict & Respond and Sense

& Respond strategies, whether an inundation occurs, and if inundation occurs, the number of

fatalities, displaced persons, and lost economic assets.

At the end of the 100-year analysis period, the present value of costs and damages are

computed using a 3 percent discount rate and the numbers of inundations, fatalities, and

displaced persons are tallied. After 10,000 iterations, statistics are generated on these model

outputs, including means, standard deviations, and medians.


4. Results

This section describes the results of our analysis of alternative strategies for adapting to sea

level rise in developing countries. We begin with a summary of the base case results that are

obtained using the input parameters as described in the preceding section. We then evaluate the

sensitivity of the results to variations in the inputs, and present a pair of sensitivity analyses for

each city.

4.1. Base Case Results

Tables 4 and 5 present the results of the simulation for, respectively, Dar-es-Salaam and

Dhaka. Results are shown for the “Do-Nothing” baseline, along with the three alternative

strategies for investing in coastal defenses. Reported costs – all discounted at 3 percent over the

100-year analysis period – include the investment cost (both capital and O&M) for coastal

defense, asset damages (the value of assets lost to inundation), and total costs (both with and

without the monetization of population impacts). In addition, the simulated number of fatalities

(not discounted) over 100 years is presented, as well as statistics on the number of years in which

inundation, economic damage, and population impacts occur. Finally, the number of times that

the defense height is increased is also reported.

In the case of Dar-es-Salaam, the Do-Nothing baseline provides the least cost approach. In

large measure, this result reflects the balance between protection costs relative to the impacts of

inundation. It highlights the prospect that in some cases, yielding to a rising sea and suffering

the associated consequences, is less expensive that investing in efforts to prevent inundation. In

other cases, however, vulnerable assets and populations (and anticipated growth thereof) are

sufficiently large to justify investments in protection. In Dhaka, for example, the Do-Nothing

baseline is not the least cost strategy. Even though it entails ongoing investments in maintaining

the existing 1.5 meter defense, doing nothing leads to repeated inundation, more than 57,000

fatalities over the 100-year analysis period, and the highest property damages of any approach.

For Dar-es-Salaam, the Inflexible Strategy, which entails a single investment in the first year

of the simulation, delivers significantly worse results than the Do-Nothing baseline, with

incremental costs of about $6.4 billion. While the Inflexible Strategy does drive down asset

damage and population impacts substantially, these savings are more than offset by an increase


Table 4 Results for Dar-es-Salaam3

Do-Nothing Baseline

Investment

Cost

Damage to Economic

Assets Total Cost

Cost with Monetization of

Population Impacts

Number of Fatalities (K)

# of Yrs w Inundation

# of Yrs w Damages

# of Yrs w Population

Impacts

# of Yrs w Increase in

Defense Height Mean $300.0 $148.2 $448.2 $1,433.0 6.1 100.0 34.9 34.9 0.0

Median $300.0 $148.1 $448.1 $1,431.9 6.2 100.0 32.0 32.0 0.0 Std Dev $0.0 $3.2 $3.2 $24.2 0.3 0.0 20.7 20.7 0.0

Inflexible Strategy

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts


Defense Height Mean $7,878.3 $1.2 $7,879.5 $7,880.2 0.05 0.01 0.01 0.01 1.00

Median $7,878.3 $0.0 $7,878.3 $7,878.3 0.00 0.00 0.00 0.00 1.00 Std Dev $0.0 $29.4 $29.4 $36.7 0.74 0.12 0.12 0.12 0.00

Real Option: Sense & Respond Strategy

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts



Median $10,522.7 $136.7 $10,659.4 $11,567.4 5.32 1.00 1.00 1.00 1.00 Std Dev $1,003.6 $3.4 $1,007.0 $1,029.6 0.13 0.01 0.00 0.00 0.01

Real Option: Predict & Respond Strategy

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts



Median $7,878.3 $0.0 $7,878.3 $7,878.3 0.00 0.00 0.00 0.00 1.00 Std Dev $60.1 $23.4 $64.4 $67.3 0.70 0.10 0.10 0.10 0.13

3 Results are for a 100-year time period simulated with 10,000 iterations. All costs are 2009 US$ millions and represent present values, computed at a 3 percent discount rate. Population impacts are monetized at $163,490 per fatality and $4,090 per displaced person.


Table 5 Results for Dhaka4

Do-Nothing Baseline

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts


Defense Height Mean $1,056.0 $1,320.3 $2,376.3 $11,147.6 57.4 100.0 14.7 14.7 0.0

Median $1,056.0 $1,309.4 $2,365.4 $11,064.4 56.0 100.0 13.0 13.0 0.0 Std Dev $0.0 $83.6 $83.6 $638.8 5.0 0.0 7.6 7.6 0.0

Inflexible Strategy

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts



Median $11,923.9 $0.0 $11,923.9 $11,923.9 0.00 0.00 0.00 0.00 1.00 Std Dev $0.0 $175.4 $175.4 $356.0 5.25 0.34 0.33 0.33 0.00

Real Option: Sense & Respond Strategy

Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts



Median $13,532.3 $786.0 $14,333.6 $19,624.8 29.44 1.00 1.00 1.00 1.00 Std Dev $3,547.4 $304.9 $3,769.3 $5,447.5 11.41 0.28 0.17 0.17 0.28


Investment

Cost

Damage to Economic

Assets Total Cost


Population Impacts



# of Yrs w Damages


Impacts



Median $6,752.7 $345.0 $7,283.5 $8,219.6 13.24 4.00 3.00 3.00 2.00 Std Dev $590.3 $425.7 $501.0 $1,312.3 16.75 4.18 2.50 2.50 0.49

4 Results are for a 100-year time period simulated with 10,000 iterations. All costs are 2009 US$ millions and represent present values, computed at a 3 percent discount rate. Population impacts are monetized at $169,960 per fatality and $4,250 per displaced person.


in investment costs of $7.5 billion. In the case of Dhaka, however, the Inflexible Strategy is

marginally more costly than the Do-Nothing baseline (i.e., $12.0 billion versus $11.1 billion),

but the mix of costs is radically different between the two scenarios. The Inflexible Strategy

entails a much large investment in coastal protection, and in turn yields much lower inundation

damages and population impacts, than does the Do-Nothing Baseline.

The two real option strategies display strikingly different results. In both cities, the Sense &

Respond Strategy has higher aggregate costs than any other approach, including doing nothing.

It also entails the highest level of investment in coastal defense, but fails to deliver a sufficient

reduction in damages to offset the costs of such investments. Largely because the Sense &

Respond Strategy is reactive in nature, investments in protection tend to be made after property

damage and population impacts have already been experienced. In Dar-es-Salaam, for example,

the Sense & Respond Strategy is about $4 billion more costly that the next most expensive

strategy. In Dhaka, it is over $8 billion more costly.

By contrast, the second real option strategy – the Predict & Respond Strategy – delivers the

best result in Dhaka. While it does not have the best performance on any one parameter –

investment cost, economic damages, or population impacts – its aggregate performance outranks

all other scenarios. The result is somewhat different in Dar-es-Salaam, where the Predict &

Respond Strategy is essentially tied with the Inflexible Strategy as the second-best performing

scenario. In Dar-es-Salaam, all of the strategies are dominated by the Do-Nothing baseline,

owing to the balance of vulnerable assets and populations relative to the costs of protection.

That notwithstanding, if policymakers in Dar-es-Salaam choose to take action, then the Predict &

Respond Strategy offers results comparable to the Inflexible Strategy, and outperforms the Sense

& Respond Strategy.

It is also instructive to compute the value of flexibility by comparing the Inflexible Strategy

to the better-performing of the two real option strategies (i.e., the Predict & Respond Strategy).

For Dar-es-Salaam, given the model inputs, there is no value to flexibility – both strategies

generate the same cost of $7.9 billion. In the case of Dhaka, however, there is substantial value

to flexibility, with the real option strategy costing $3.4 billion less ($8.6 billion versus $12.0

billion) than the Inflexible Strategy – a savings of about 28%.


In sum, depending on local circumstance, the Do-Nothing baseline may provide the optimal

result. In all cases, the second real option strategy (Predict & Respond) outperforms the first real

option strategy (Sense & Respond). It is also comparable to, or outperforms, the Inflexible

Strategy, which makes significant up-front investments in coastal defense, but does not always

yield reductions in economic damages and population impacts sufficient to offset those

investments. In addition, depending on local conditions, a flexible real option strategy may yield

substantial savings relative to an inflexible approach.

4.2. Results of Sensitivity Analyses

In order to better understand the potential value of flexible strategies for adapting to sea level

rise, we developed two alternative scenarios for model inputs, each of which was applied to the

simulation of inundation events in the two cities. The first scenario focused on changes in

conditions on the land-side of the coastal defense. For this scenario, asset values are assumed to

be both more variable and faster growing, with a mean of 5% and a standard deviation of 4% (as

opposed to, respectively, 4% and 2% in the base case). Population growth was assumed to be

more variable, with the two bounds of the triangular probability distribution extended by an

amount equal to half the initial minimum rate (which was 1.91% for Dar-es-Salaam and 0.76%

for Dhaka). The value of a statistical life, and by extension the value of a displaced person, was

increased by 50%. Finally, the cost of constructing and maintaining coastal defenses was

decreased by one-third, yielding a unit cost of $3,745 and an O&M cost of 2.67% of invested

capital. Taken together, this set of changes to the simulation inputs is meant to represent a

situation where the value of protection is both increased and made more variable while the cost

of that protection is lower.

The second alternative scenario focuses on the prospect of more significant climate change

than simulated in the base case. The mean global sea level rise is assumed to be 5mm/year rather

than 3mm/year, and the standard deviation is assumed to be 4mm/year, rather than 2mm/year. In

addition, the extreme value distribution for sea surges was adjusted to increase the probability of

more extreme sea levels. In particular, the scale factor (!) was increased by a factor of five, from

0.08 to 0.40 for Dar-es-Salaam and from 0.225 to 1.125 for Dhaka. The effect of this change on,

for example, Dar-es-Salaam is to raise the height of the 100-year event from 3.1m to 4.6m while

leaving the height of the 1-year event unchanged and the mean surge height about 0.2m higher.


The height of the 100-year event in Dhaka is increased from 4.7m to 8.9m. Again, the height of

the 1-year event is unchanged; the mean surge height is about 0.5m higher.

In conducting the sensitivity analyses, no changes beyond those described above were made

to the model inputs. Each of the sensitivity scenarios was applied separately; that is, we did not

consider a case where both the land-side changes and climate changes were considered

simultaneously. Table 6 presents the highlights of the sensitivity analyses.

When it comes to the sensitivity analysis of land-side economic factors, we observe that costs

drop in both cities under all strategies, although not for the Do-Nothing baseline. In the Do-

Nothing baseline, there is no new investment in coastal defenses, so unsurprisingly the assumed

reduction in unit construction cost has no impact; instead, the increase in asset values and

populations means that inundation has a higher cost which, in turn, causes the aggregate cost of

the Do-Nothing baseline to rise. In all other scenarios, however, total costs decrease despite the

increase in vulnerability, suggesting that the unit protection costs are an important driver of the

analytic results. In turn, successful research into methods for constructing lower cost, yet still

effective, coastal defenses would be valuable.

When it comes to the sensitivity analysis of greater climate change, results for the two cities

differ markedly. Total costs do increase in both cities under all scenarios, an unsurprising result

owing to the increase in the height and frequency of storm surges, but the effect in Dhaka is

more pronounced than in Dar-es-Salaam. Under the Inflexible Strategy, for example, costs

increase by about 80% (from $7.9 to $14.2 billion) in Dar-es-Salaam, but in Dhaka, costs go up

by about 338% (from $12.0 to $52.6 billion). While cost increases are negligible for two of the

four scenarios in Dar-es-Salaam under greater climate change, costs in Dhaka rise by a factor of

about four in all scenarios, suggesting that vulnerability to higher seas is much higher in Dhaka.

Finally, the sensitivity analyses demonstrate the connection between climate change and the

value of flexibility. In Dar-es-Salaam, for example, we observe no value to flexibility in the base

case or in the sensitivity case where the land-side parameters are varied. In the face of more

significant and variable sea level rise, however, the value of flexibility jumps markedly, to $4.6

billion. The effect is even more pronounced in Dhaka, where the value of flexibility jumps from

$3.4 billion in the base case to over $15 billion in the sensitivity analysis where the climate

changes more significantly.


Table 6 Sensitivity Analyses:

Total Cost by Scenario5

Scenario

Dar-es-Salaam Dhaka

Base Case

Increased Vulnerability

& Lower Protection

Cost

Greater Climate Change

Base Case

Increased Vulnerability

& Lower Protection

Cost

Greater Climate Change

Do-Nothing Baseline $1.4 $1.8 $1.5 $11.1 $14.9 $43.5

Inflexible Strategy $7.9 $4.2 $14.2 $12.0 $6.4 $52.6

Real Option: Sense & Respond Strategy $11.8 $7.3 $11.8 $20.4 $16.3 $85.5


$7.9 $4.3 $9.5 $8.6 $5.9 $37.5

Value of Flexibility6 $0.0 $0.0 $4.6 $3.4 $0.6 $15.1

5 Results are mean values from a simulation of 10,000 iterations. All costs are 2009 US$ millions and represent the present value of costs incurred over a 100 years, computed at a 3 percent discount rate. Population impacts are monetized as described in the text. 6 Value of flexibility is defined as the maximum of $0.0 and the difference between the cost of the Inflexible Strategy and the cost of the Real Option: Predict & Respond Strategy.


4.3. Limitations of Our Analysis

Before moving to a discussion of our analytic results, it is important to quickly take stock of

some of the key limitations to our approach, virtually all of which originate in the simplifying

assumptions made in order to render the analysis tractable. Some of these assumptions relate to

the characteristics of the coastal defense where we assume that construction can be completed

within a single year, that land is readily available for the widening of the base of the defense

when its height is increased, and that the only pathway to inundation is from the over-topping of

the defense rather than its outright failure. When it comes to development patterns, we did not

simulate a behavioral link between policy decisions about coastal defense and the location

decisions of firms and residents. Presumably, a stronger coastal defense system would increase

the propensity to locate in lower elevations while a policy decision to minimize or defer

protection might induce some firms or residents to locate outside vulnerable areas. Finally, we

modeled climate change in a rather simple fashion by, for example, assuming a constant century-

long trend in the annual change in global sea levels (albeit with variability around that central

tendency), by assuming that local sea level change (i.e., either subsidence or uplift) is constant,

by assuming that the parameters underlying the extreme value distribution for characterizing

storm surges are constant, and by assuming no abrupt change in global sea levels as might be

caused, for example, by a sudden collapse of the West Antarctic Ice Shelf.

5. Discussion

5.1. Implications for Local Planning Decisions

Our analysis has several interesting implications for local planning initiatives to defend a

coastal city from rising sea levels. First, real option strategies that provide flexibility have the

potential to materially reduce aggregate costs. This cost advantage originates from two factors.

The first is that, in contrast to an inflexible strategy where the protection height is selected once

at the outset of the policy process, the flexible strategy holds out the chance that in some cases,

sea level rise may not be as significant as initially thought, or that the size of the vulnerable

assets and populations may be lower. In such cases, then, less robust defenses are needed and

investment costs can be lower than with an inflexible strategy. The second source of a flexible

strategy’s cost advantage comes from the opportunity to defer investment. If planners are able to


postpone construction costs by even say, twenty years, then the present value cost drops by about

45 percent (at a discount rate of 3 percent).

In Dhaka, the value of flexibility is convincingly demonstrated in both the base case and the

sensitivity case for greater climate change where the Predict & Respond real option cuts costs

relative to the Inflexible Strategy by, respectively, $3.4 and $15.1 billion. Given Bangladesh’s

2009 GDP of $208.6 billion (PPP), these savings are material (World Bank Databank, 2011).

Flexibility has less immediate value in the case of Dar-es-Salaam where the Predict & Respond

Strategy yields savings over the Inflexible Strategy only in the case of greater climate change

than simulated in the base case. In that instance, however, the value of flexibility is $4.6 billion

– a not insignificant share of Tanzania’s PPP-adjusted GDP of $57.9 billion (World Bank

Databank, 2011).

These results are consistent with traditional methods of valuing financial options in which

two of the important drivers of option value are the price of the underlying asset and the

volatility of that price. Increases in either parameter lead to higher option valuations (Hull,

2009). When it comes to sea level rise, the underlying real asset is the protection afforded by the

coastal defenses. As sea levels rise more quickly and large surges become more frequent – as

seen in the sensitivity case where the mean annual rise is increased from 3mm to 5mm and the

Gumbel extreme value distribution is scaled up – the value of protection increases, making the

real option more valuable. In addition, just like a stock option that becomes more valuable when

the price of the underlying stock becomes more volatile, the value of the real option for

protecting against sea level rise becomes more valuable when the standard deviation of the trend

in global sea level rise is doubled from 2mm/year to 4mm/year. The value of flexibility (i.e., of

the Predict & Respond Strategy relative to the Inflexible Strategy) is highest for both cities in the

sensitivity case with greater climate change.

Another implication of our analysis is that flexibility sometimes comes with a high price. As

clearly demonstrated by the Sense & Respond strategy, if a city postpones investments in coastal

defense until rising seas clearly threaten its existing defenses, it may end up waiting too long to

protect itself and may incur devastating inundations as a result. This risk therefore must be

balanced against the potential cost savings of delaying investments in protective measures.


This finding underscores an important point: not all real option strategies are inherently

superior to inflexible strategies. The real option strategy must be structured so that the resolution

of uncertainty occurs with sufficient time to allow the option holder to make a well-reasoned

decision about whether to exercise the option. For example, a financial investor holding a call

option on a stock learns about the value of the underlying asset by observing the stock price on

the date of option expiration. He or she can then determine whether exercising the option would

be profitable. In contrast, if a local government holding a real option to increase the height of its

coastal defense learns about the value of the protection only in the aftermath of a catastrophic

flood, then the value of the flexibility must be decremented by the value of the losses incurred.

Finally, we observe that the quality of the information that is being obtained over time – the

source of a real option’s potential to create value – has an important bearing on the option’s

value. The superior performance of the Predict & Respond strategy for example is due, in large

measure, to the increasingly accurate prediction of sea levels over the 100-year analysis period.

In year 61, for example, local planners have 60 prior years of observation to better understand

the trajectory of global sea level rise. This information, however, never enters the decision

calculus under the Inflexible strategy.

Predictions of sea level rise do not, of course, come only from local planners. Indeed, the

scientific community has a vitally important role to play here. While projections of total sea

level rise over the next century are important to decisions about global climate policy, they are

only relevant to local planning decisions if an inflexible, single-investment, strategy is being

considered with the goal of constructing a coastal defense sufficient for a century’s worth of sea

level rise. If, on the other hand, local planners aspire to implement a cost-minimizing real option

strategy, then their information needs are markedly different from those of global policymakers.

The time period for which they need projections of sea level rise would be much shorter –

perhaps only 20 to 40 years. Projections over longer time frames would not be needed, since

optional increases in sea level defenses can be used by planners in later years to address

subsequent sea level rise should it actually occur.

Another important piece of information that would enhance the local planning effort is the

rate of local sea level rise. Subsidence, caused either by human activity such as ground-water

withdrawal or by natural process, or increases in land elevation, caused by tectonic uplift or


sediment deposition, can have a significant on the local consequences of global sea level rise.

The former would exacerbate global sea level rise while the latter would mitigate it. In

conducting the background research for this study, we discovered that reliable data on local sea

level rise in developing countries appear to be sparse.

Especially important for local planning efforts is not just the mean, or expected value, of

potential sea level rise in the next few decades, but also estimates of the nature and width of the

dispersion around the mean. Perhaps the largest challenge in using a real option approach to

constructing coastal defenses is the possibility that such defenses will be over-topped (because

they have been built to a lower height than under an inflexible strategy), leading to inundation.

With information on variability, planners can assess the risk of over-topping prior exercising the

option to raise the coastal defense and balance such risks against potential savings in protection

costs. If information is only available on the central tendency, and not the dispersion, of

expected sea level rise, then this balancing cannot be done.

5.2. Implications for Policy Makers

Beyond the relative economic merits of inflexible and real option strategies for adapting to

climate change, there also exist at least two pragmatic considerations that are relevant to the

choice between the two strategies. The first relates to the in-country institutional capability to

manage a real option strategy and the second involves the practical realities of international

development assistance for adaptation to climate change.

5.2.1. Institutional Capability to Manage a Real Option

The process of a managing a real option strategy is likely to be much more complex than

implementing an inflexible strategy. While ongoing maintenance of the coastal defense would

be needed in either case to prevent deterioration of its protective capability, the inflexible

strategy has a “once and forget it” character that is lacking for the real option strategy. With the

real option strategy, changes in local sea conditions and in the scientific predictions of future sea

level rise must be monitored on an ongoing basis. Changes in the value of economic assets and

vulnerable populations on the land-side of the defenses must also be regularly assessed in order

to re-calibrate the value of protection. In turn, sequential decisions must be made about whether

changing circumstances warrant a fortification of the coastal defense. If a decision to improve

the defense is taken, another series of activities must be launched: project design, bid


solicitation, vendor selection, land acquisition (if needed), construction management, and so

forth. For the real option strategy to realize its potential value, the local planning authorities

must have the institutional capacity to execute all these activities successfully and to do so in a

timely fashion. If such capacity is lacking, the result may be an insufficiently robust coastal

defense structure.

5.2.2. Financial Resources for Future Exercise of Option

Beyond these institutional considerations, the use by a developing country of a real option

approach for structuring its investments in adaptation to climate change may have important

implications for international development assistance, such as that provided by the Global

Environment Facility or the UNFCCC Adaptation Fund. Unlike a one-off project to construct a

coastal defense structure, the real option approach contemplates capital investments on an

ongoing basis over several decades. Both funders and recipients of development assistance

would therefore need to address the question of how much funding is necessary and when it

should be disbursed. In short, the same uncertainty that makes the real option approach

attractive creates a dilemma for funders and recipients: the level and timing of funding needed to

exercise the option at various intervals would not be known until much later in time. In contrast,

an inflexible strategy that entails immediate construction of a coastal defense would likely be

more expensive than a real option strategy, but it has the advantage that it can be designed,

financed, and built in a relatively short timeframe.

Most multilateral financial mechanisms are funded in tranches that extend only over a few

years; it is easy to imagine that the need for funding to exercise an option could occur after funds

in a particular tranche have been exhausted. A recipient country might understandably be

reluctant to pursue a real option strategy if there were a chance that the funding for subsequent

improvements in the coastal defense would be unavailable. One alternative might be for the

funding source to put the monies in an escrow account that could be tapped at the recipient

country’s discretion, thereby creating the certainty of future funding to exercise the option. An

interesting codicil to this observation is that, owing to the possibility that the option will not be

exercised (if sea level rise, asset appreciation, or population growth is lower than expected), such

escrowed funds might never be needed. Policies and mechanisms for handling such

contingencies would need to be developed.


6. Conclusion

6.1. Next Steps

The foregoing analysis suggests several possible avenues for future research. As mentioned

previously, addressing the subject of risk aversion, and whether and how it should be handled in

analyzing adaption to climate change is one area for further investigation. In addition,

addressing the limitations of the simulation model that were described in Section 4.3 above

would make for a more robust set of results, as would applying the model to other locations. We

also anticipate using the analytic framework to better understand the key scientific, economic,

and policy information that is needed to improve the quality of sequential decision making about

adaptation to rising sea levels. Doing so would, in turn, allow us to characterize the economic

value of research to improve the quality of that information. Finally, an understanding of the

degree to which findings drawn from the field of sea level rise can be generalized to adaptation

to other types of climate impacts would be valuable.

6.2. Summary

Developing countries face large potential costs for adapting to climate change and must make

investment decisions in the context of limited resources and competing development priorities.

Accordingly, investment strategies that minimize such costs are particularly valuable. This

analysis demonstrates that, at least with respect to sea level rise, framing and valuing adaption

decisions as real options has the potential to materially reduce costs to developing countries.

This finding is not a universal one because, in some cases, the local relationship among sea

levels, coastal features, protection measures, and vulnerable assets and population means that

there is little value to be gained with a flexible approach. That said, in some locations and under

conditions of high uncertainty, the flexibility to postpone even some adaptation investments until

more information is obtained and uncertainty is reduced, can create substantial cost savings. The

analysis also points to certain types of information as particularly valuable for decision makers,

such as predictions of sea level rise over two or three decades rather than a century or more, an

estimate not just of the central tendency of future sea level rise but also about the potential

variability of that estimate, and the rates of local sea level rise for specific locations. Finally, we

observe that despite the potential economic value of real option strategies, several policy and

institutional issues must be addressed before such potential value can be realized.


Works Cited Arrow, K., & Lind, R. (1970). Uncertainty and the Evaluation of Public Investment Decisions. The American Economic Review , 60 (3), 364-378.

Boardman, A., Greenberg, D., Vining, A., & Weimer, D. (2006). Cost Benefit Analysis: Concepts and Practices, 3e. Upper Saddle River, NJ: Pearson Prentice Hall.

Bureau of Meteorology. (2011). ARI and AEP Explained. Retrieved March 27, 2011, from Government of Australia: www.bom.gov.au/hydro/has/ari_aep.shtml

Copeland, T., & Antikarov, V. (2003). Real Options: A Practitioner's Guide. New York: Cengage.

Dasgupta, S., Laplante, B., Murray, S., & Wheeler, D. (2009). Sea-Level Rise and Storm Surges: A Comparative Analysis of Impacts in Developing Countries. Environment and Energy Team, Development Research Group. Washington, DC: The World Bank.

Dobbes, L. (2010). Notes on Applying 'Real Options' to Climate Change Adaptation Measures, with Examples from Vietnam. Crawford School of Ecconomics and Government, Centre for Climate Economics & Policy. Canberra: Australian National University.

H.M. Treasury. (2009). Accounting for the Effects of Climate Change: Supplementary Green Book Guidance.

Hertzler, G. (2007). Adapting to Climate Change and Managing Climate Risks by Using Real Options. Australian Journal of Agricultural Research , 58, 985-992.

Hillen, M., Jonkman, S., Kanning, W., Kok, M., Geldenhuys, M., & Stive, M. (2010). Coastal Defence Cost Estimates. Delft University of Technology.

Hull, J. (2009). Options, Futures, and Other Derivativesq (7th ed.). Upper Saddle River, NJ: Perason Education.

IPCC. (1990). Policymakers Summary prepared by Working Group 1. In J. Houghton, G. Jenkins, & J. Ephraums, Climate Change: The IPCC Scientific Assessment. Cambridge, UK: Cambridge University Press.

IPCC. (2007a). Summary for Policy Makers. In M. Parry, O. Canaiani, J. Palutkof, P. v. Linden, & C. Hanson, Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report. Cambridge, UK: Cambridge University Press.

IPCC. (2007b). Summary for Policy Makers. In S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. Avery, et al., Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report. Cambridge, UK: Cambridge University Press.

IPCC. (2007c). Synthesis Report. In R. Pachauri, & A. Reisinger, Climate Change 2007: Contribution of Working Groups I, II, and III to the Fourth Assessment Report. Geneva, Switzerland: Intergovernmental Panel on Climate Change.

IPCC. (2007d). Technical Summary. In M. Parry, O. Canaiani, J. Palutkof, P. v. Linden, & C. Hanson, Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report. Cambridge, UK: Cambridge University Press.

IPCC. (2010). Fifth Assessment Report. Retrieved February 1, 2011, from IPCC - Activities: http://www.ipcc.ch/activities/activities.htm

Kebede, A., & Nicholls, R. (2011). Population and Assets Exposed to Coastal Flooding in Dar-es-Salaam (Tanzania). University of Southampton. Global Climate Adaptation Partnership.


Kotz, S., & Nadarajah, S. (2000). Extreme Value Distributions: Theory and Applications. London: Imperial College Press.

Lowe, J., & Gregory, J. (2010). A Sea of Uncertainty. Nature Reports Climate Change , 4, 42-43.

Mendelsohn, R., Dinar, A., & Williams, L. (2006). The Distributional Impact of Climate Change on Rich and Poor Countries. Environment and Development Economics , 11, 159-178.

Miller, T. R. (2000). Variations between Countries in Values of Statistical Life. Journal of Transport Economics and Policy , 34 (2), 169-188.

Milliman, J., & Haq, B. (1996). Sea-Level Rise and Coastal Subsidence: Casues, Consequences, and Strategies. Boston: Klewer Academic Publishers.

National Research Council. (2010). Advancing the Science of Climate Change. Washington, DC: The National Academies Press.

Ng, W.-S., & Mendelsohn, R. (2005). The Impact of Sea Level Rise on Singapore. Environment and Development Economics , 10, 201-215.

Nicholls, R., Hanson, S., Herweijer, C., Patmore, N., Hallegatte, S., Corfee-Morlot, J., et al. (2008). Ranking Port Cities with High Exposure and Vulnerability to Climate Extremes: Exposure Estimates. OECD Environment Working Papers. OECD Publishing.

Population Division of the Dept of Economic and Social Affairs of the United Nations Secretariat. (2008). World Population Prospects. Retrieved April 28, 2011, from The 2008 Revision Population Database: esa.un.org/unpp/p2k0data.asp

Rahmstorf, S. (2010). A New View on Sea Level Rise. Nature Reports Climate Change , 4, 44-45.

Scandizzo, P. (2010). Adapting to Climate Changes: How to Evaluate Strategies and Projects. Saarbrucken, Germany: VDM Verlag.

Shockley, R. (2007). An Applied Course in Real Options Valuation. Mason, OH: Thomson Higher Education.

Subsidiary Body for Scientific and Technological Advice. (2010). Report on the Technical Workshop on Costs and Benefits of Adaptation Options. Cancun, Mexico: United Nations Framework Convention on Climate Change.

Triantis, A. (2003). Real Options. In D. Logue, & J. Seward, Handbook of Modern Finance (pp. D1-D32). New York: Research Institute of America.

Triantis, A. (2001). Real Options: State of the Practice. Journal of Applied Corporate Finance , 14 (2), 8-24.

U.S. Council of Economic Advisors. (2011). Economic Report of the President. Table B-7.

Valfedis, A., Boot, G., Cox, J., Maatens, R., McFadden, L., Nicholls, R., et al. (n.d.). Diva Database Documentation. Retrieved May 2, 2011, from www.civil.soton.ac.uk/diva

Vonortas, N. S., & Desai, C. A. (2007, 12). A "Real options" framework to assess public research investments. 34 (10), pp. 699-708.

Weyant, J. (2008). A Critique of the Stern Review's Mitigation Cost Analyses and Integrateed Assessment. Review of Environmental Economics and Policy , 2 (1), 77-93.

Woodward, M., Gouldby, B., Kapelan, Z., Khu, S., & Townend, I. (2010). Incorporating Real Options into Flood Risk Management Decision Makingn. 14th Annual International Real Options Conference. Rome.


World Bank Databank. (2011). Retrieved May 3, 2011, from databank.worldbank.org

World Bank. (2010). Economics of Adaptation to Climate Change: Synthesis Report. Washington, DC.

World Bank. (2009). Mainstreaming Adaptation to Climate Change in Agriculture and Natural Resources Management Projects, Guidance Note 7, Annex 12. Environment Department.

Yohe, G., Neumann, J., & Marshall, P. (1999). The Economic Damage Induced by Sea Level Rise in the United States. In R. Mendelsohn, & J. Neumann, The Impact of Climate Change on the United States Economy (pp. 178-208). Cambridge, UK: Cambridge University Press.

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