Technical Policy Briefing Notes - 4
Real Options Analysis
Case Studies
Policy Briefs
Real Options Analysis
Case Studies
The MEDIATION study has reviewed existing
literature examples that have applied ROA to a
number of adaptation case studies. A number of
these case studies are summarised in the box
below.
Case Study 1:
Real Options Analysis – Generic Guidance
The practical application of ROA to adaptation is limited, with only a few examples to date. HMT (2009) provides a simplified theoretical example, which is incorporated into supplementary Government guidance on economic appraisal for adaptation. This recognises that there may be activities (or options) with the flexibility to upgrade in the future, and that these provide an option to deal with more (or less) severe climate change in light of information from learning or research. It presents an example using sea wall defence and sets out the use of decision trees to understand the sequence of actions and decision points. Similar to the simplified example above, it uses two alternative options: investing now in a large sea wall defence versus investing a wall which has the potential to be upgraded in the future. The NPV of these investments is assessed under low and high future sea level rise scenarios (hypothetical), estimating the expected value and assuming equal chance of low and high climate change. The analysis can therefore compare a standard investment against an upgradeable wall, the latter with the flexibility to be upgraded in the future if higher levels of sea level rise emerge.
In the example, the standard wall costs 75, and has benefits of 100 from avoided flooding. The upgradeable wall costs 50, the upgrade costs 50 and would give benefits of 200 from avoided flooding. For the standard investment, the NPV is -25 (=0.5*25 + 0.5*-75), which suggests the investment should not proceed. For the upgradable wall, then an extended decision tree is considered. If the impacts of climate change are high enough to warrant upgrading, then the value of the investment is 120. If the impacts are low, then upgrading is not justified as the payoff is negative (-40), but since the investment costs of the upgrade are not needed in practice in the low outcome, they are not incorporated into the NPV. The expected value of investing now with the option to upgrade in the future is therefore +10 (=0.5*(120) – 50). Comparing the two options shows an NPV of -25 for the standard wall, and +10 for the flexible wall, thus flexibility to upgrade in the future is reflected in the higher NPV, and switches the investment decision.
In practice, this example does not reflect the complexity or challenges involved with real world decisions, e.g. the complex uncertainty over sea level rise scenarios (including changes in storm surge risks), the level of detail on costs and the quantitative and economic analysis of benefits.
The practical application of ROA to adaptation is limited, with only a few examples to date. HMT (2009) provides a simplified theoretical example, which is incorporated into supplementary Government guidance on economic appraisal for adaptation. This recognises that there may be activities (or options) with the flexibility to upgrade in the future, and that these provide an option to deal with more (or less) severe climate change in light of information from learning or research. It presents an example using sea wall defence and sets out the use of decision trees to understand the sequence of actions and decision points. Similar to the simplified example above, it uses two alternative options: investing now in a large sea wall defence versus investing a wall which has the potential to be upgraded in the future. The NPV of these investments is assessed under low and high future sea level rise scenarios (hypothetical), estimating the expected value and assuming equal chance of low and high climate change. The analysis can therefore compare a standard investment against an upgradeable wall, the latter with the flexibility to be upgraded in the future if higher levels of sea level rise emerge.
In the example, the standard wall costs 75, and has benefits of 100 from avoided flooding. The upgradeable wall costs 50, the upgrade costs 50 and would give benefits of 200 from avoided flooding. For the standard investment, the NPV is -25 (=0.5*25 + 0.5*-75), which suggests the investment should not proceed. For the upgradable wall, then an extended decision tree is considered. If the impacts of climate change are high enough to warrant upgrading, then the value of the investment is 120. If the impacts are low, then upgrading is not justified as the payoff is negative (-40), but since the investment costs of the upgrade are not needed in practice in the low outcome, they are not incorporated into the NPV. The expected value of investing now with the option to upgrade in the future is therefore +10 (=0.5*(120) – 50). Comparing the two options shows an NPV of -25 for the standard wall, and +10 for the flexible wall, thus flexibility to upgrade in the future is reflected in the higher NPV, and switches the investment decision.
In practice, this example does not reflect the complexity or challenges involved with real world decisions, e.g. the complex uncertainty over sea level rise scenarios (including changes in storm surge risks), the level of detail on costs and the quantitative and economic analysis of benefits.
Case Study 2:
Real Options Guidance – Moving to Practice
The previous example is relatively straightforward to solve because: only four investment options are considered, either invest in a standard/upgradeable wall, with one sequential decision to upgrade; there are only two decision points, i.e.: at t0, and at the upgrading moment; only two possible uncertain future states of the world can be realised, either ‘high’, or ‘low’ climate change impacts; the timing of learning is known; and at this time, uncertainty is fully resolved. A more realistic case study looking at the optimal dike height under uncertainty with learning about climate change impacts is therefore presented below.
Dike heightening is expensive, and economically efficient investment is therefore important. Van Dantzig (1956) described that dike investment is a cost minimisation problem, after a large flooding in the Netherlands in 1953. In essence, higher dikes reduce expected damage costs, but investment costs increase exponentially with dike height. A balance has to be found between expected damages and costs of dike construction over time, noting decisions on dike height are recurrent for a number of reasons (e.g. economic growth, climate change impacts on water levels, or soil subsidence). On the one hand, it is not optimal to build a dike once and for all because that would result in excessive investment costs with only little benefits. On the other hand, dike heightening, like most large investment, has fixed costs, and therefore, yearly investment is not optimal but rather a solution where a dike is revised at longer time intervals, for example, half a century.
Crucial to determine optimal dike height over time are water level observations. With these observations return periods of different water levels can be estimated. Water defences protecting land from large-scale flooding events typically offer protection against events with long return periods (e.g. 10000 years or even more), but these events are extremely rare, though they will become less rare in the future due to climate change.
With climate change, sea levels are expected to rise, and peak river discharges are expected to increase. These future scenarios have been projected, but are insufficient to be valuable for a costbenefit approach, as they require information on possible future states of the world and also probabilities of these states. In the Bayesian literature these probabilities are called informed priors, or subjective probabilities. So far, subjective probability distributions are lacking for the rate of sea level rise or the increase in peak discharges although that it is clear to some scenarios are much less likely than others. A second problem is that we poorly understand how / what / when we will learn about climate change impacts. Some sources of uncertainty are likely to be reduced: water level observations will grow, reducing statistical uncertainty, and model structure uncertainty is likely to be reduced over time with research. If we know that better information will be available in the future, this may have implications for current dike heightening decisions. As explained previously, information has expected value: once we know better dike heightening strategy can be adapted to reduce total expected costs.
Nonetheless, with some prior distribution about the rate of the structural water level increase, that is the speed with which the relative water level is structurally increasing, and assumptions about the learning process, it is possible to investigate the problem of optimal dike height, and how valuable it is to obtain better knowledge on climate change impacts for the dike heightening problem: that is the expected costs savings that can be obtained by anticipating new information, and by changing the dike heightening strategy once information has been received. Furthermore, early information is more valuable than late information because future costs are discounted. For this case study, we introduce a special case of learning: perfect learning, which we assume to be a probabilistic event following a survival model. The decision variable is the dike increment , ut, the amount with which the dike is heightened, at any time t. The problem is discretised in small time steps , tk, and the decision space is discretised as well, utk, E{0, Δu, 2Δ u ,.., umax}. The left panel of Fig.1 shows a decision tree with the various trajectories of dike heightening over time. The right panel in Fig.1 shows an event tree: at every time step it is possible that perfect information is received on the rate of the structural water level increase. Once perfect information has been received, we are back to an original deterministic problem setting, which has been studied by Eijgenraam et al. (2012).
The above problem is solved with dynamic programming. The procedure is similar to the previous example: for every probability weighted state expected costs are calculated, and the optimal dike heightening strategy is found with in a backward-forward procedure.
Case results indicate that current and short-term dike heightening decisions are weakly affected by future learning. Perceptions about the likelihood of climate change impacts are very relevant for current decision making. Optimal dike heightening strategies change significantly if different priors for the rate of the structural water level increase are taken. The expected value of information can be substantial.
For more information, see:
The previous example is relatively straightforward to solve because: only four investment options are considered, either invest in a standard/upgradeable wall, with one sequential decision to upgrade; there are only two decision points, i.e.: at t0, and at the upgrading moment; only two possible uncertain future states of the world can be realised, either ‘high’, or ‘low’ climate change impacts; the timing of learning is known; and at this time, uncertainty is fully resolved. A more realistic case study looking at the optimal dike height under uncertainty with learning about climate change impacts is therefore presented below.
Dike heightening is expensive, and economically efficient investment is therefore important. Van Dantzig (1956) described that dike investment is a cost minimisation problem, after a large flooding in the Netherlands in 1953. In essence, higher dikes reduce expected damage costs, but investment costs increase exponentially with dike height. A balance has to be found between expected damages and costs of dike construction over time, noting decisions on dike height are recurrent for a number of reasons (e.g. economic growth, climate change impacts on water levels, or soil subsidence). On the one hand, it is not optimal to build a dike once and for all because that would result in excessive investment costs with only little benefits. On the other hand, dike heightening, like most large investment, has fixed costs, and therefore, yearly investment is not optimal but rather a solution where a dike is revised at longer time intervals, for example, half a century.
Crucial to determine optimal dike height over time are water level observations. With these observations return periods of different water levels can be estimated. Water defences protecting land from large-scale flooding events typically offer protection against events with long return periods (e.g. 10000 years or even more), but these events are extremely rare, though they will become less rare in the future due to climate change.
With climate change, sea levels are expected to rise, and peak river discharges are expected to increase. These future scenarios have been projected, but are insufficient to be valuable for a costbenefit approach, as they require information on possible future states of the world and also probabilities of these states. In the Bayesian literature these probabilities are called informed priors, or subjective probabilities. So far, subjective probability distributions are lacking for the rate of sea level rise or the increase in peak discharges although that it is clear to some scenarios are much less likely than others. A second problem is that we poorly understand how / what / when we will learn about climate change impacts. Some sources of uncertainty are likely to be reduced: water level observations will grow, reducing statistical uncertainty, and model structure uncertainty is likely to be reduced over time with research. If we know that better information will be available in the future, this may have implications for current dike heightening decisions. As explained previously, information has expected value: once we know better dike heightening strategy can be adapted to reduce total expected costs.
Nonetheless, with some prior distribution about the rate of the structural water level increase, that is the speed with which the relative water level is structurally increasing, and assumptions about the learning process, it is possible to investigate the problem of optimal dike height, and how valuable it is to obtain better knowledge on climate change impacts for the dike heightening problem: that is the expected costs savings that can be obtained by anticipating new information, and by changing the dike heightening strategy once information has been received. Furthermore, early information is more valuable than late information because future costs are discounted. For this case study, we introduce a special case of learning: perfect learning, which we assume to be a probabilistic event following a survival model. The decision variable is the dike increment , ut, the amount with which the dike is heightened, at any time t. The problem is discretised in small time steps , tk, and the decision space is discretised as well, utk, E{0, Δu, 2Δ u ,.., umax}. The left panel of Fig.1 shows a decision tree with the various trajectories of dike heightening over time. The right panel in Fig.1 shows an event tree: at every time step it is possible that perfect information is received on the rate of the structural water level increase. Once perfect information has been received, we are back to an original deterministic problem setting, which has been studied by Eijgenraam et al. (2012).
Figure 1: Dike height decisions
over time graphically illustrated (left panel), and event tree showing
probabilistic learning (right panel).
The above problem is solved with dynamic programming. The procedure is similar to the previous example: for every probability weighted state expected costs are calculated, and the optimal dike heightening strategy is found with in a backward-forward procedure.
Case results indicate that current and short-term dike heightening decisions are weakly affected by future learning. Perceptions about the likelihood of climate change impacts are very relevant for current decision making. Optimal dike heightening strategies change significantly if different priors for the rate of the structural water level increase are taken. The expected value of information can be substantial.
For more information, see:
- van der Pol, T.D., van Ierland, E.C. and Weikard, H.-P. (2013) Optimal Dike Investments under Uncertainty and Learning about Increasing Water Levels. Journal of Flood Risk Management (under review)
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