KR101927898B1 - Method for Building Decision Tree Model Based on Real Option Analysis Considering Uncertainty of Climate Change - Google Patents

Abstract

The present invention relates to a method for building a decision tree model based on real option analysis considering the uncertainty of climate change. The method for building a decision tree model based on real option analysis considering the uncertainty of climate change includes: a step of estimating a storage amount; a step of estimating drought damage and drought reduction amounts; and a step of analyzing and outputting a scenario.

Description

(Decision Tree Model Based on Real Option Analysis Considering Uncertainty of Climate Change Based on Uncertainty of Climate Change)

The present invention focuses on adaptive decision making and reflects the uncertainty of climate change in the most real options analysis method and provides realistic option analysis based on uncertainty of climate change to reevaluate economic analysis of water supply policy for drought And a method for constructing a decision tree.

Abnormal climate change is a task of mankind that can not be delayed anymore, and it is a phenomenon we face now, not a long time later. It is becoming increasingly difficult to prepare for natural disasters such as extreme droughts or floods. Furthermore, failure to control water supply or water shortage due to rapid climate change is a cause for adaptation of water policy related to water quality, water quality and water quality. Recent extreme droughts in the western part of Chungcheongnam province are a simple example of adaptation of water policy to climate change. In order to cope with such a drought, it is necessary to plan the investment of alternative water resources projects. In addition to large project costs, it is a long-term plan. As an approach to this, decision making methods are being raised under uncertainty.

In the case of the cash flow discount method, which is a traditional decision-making method, it is assumed that the investment of the business is immediately proceeded. In addition, since the cash flow discounting method assumes certainty, it is difficult to adopt the cash flow discounting method as a valuation method if forecasts such as uncertainty due to climate change are not available. In this paper, we propose that the real option evaluation method used in economics can be approached in engineering, and if the uncertainty is well defined, the real option option Will become more applicable.

In order to establish a water resource strategy that takes climate uncertainty into consideration, developed countries have been actively studying methods of planning for doctoral support for the past 10 years. All of these studies emphasize robust and adaptive decision making. Domestic decision - making methods have been studied under uncertainty, but adaptation studies in the water resources field are still in the early stages.

As a prior art related to the present invention, a real option-based investment decision method for improvement of a city water pollution disaster prevention system performed by a computer in Patent Document 1 is a method for determining investment based on current options Calculating a value; Calculating the variability of the value of the urban water pollution disaster prevention system from the statistical distribution of the past flood damage data; And for each of the alternatives, the present value of the benefit of each alternative is used as an underlying asset, and the delay period until the actual execution timing of each alternative expires, And calculating the value of the execution time strategy of the above alternatives as the value of the calculated call option, in order to improve the urban disaster prevention system in consideration of climate change.

Korean Patent Laid-Open Publication No. 10-2014-0134084 (published on November 21, 2014)

In view of the above circumstances, the present invention is based on adaptive decision making, in which the most real option analysis method is applied to a wide range of uncertainties, The purpose of the analysis is to identify and revalue the value of the economy.

In order to achieve the above object, (a) if future inflow data is generated in the future inflow data generation module using the observed inflow data from the collected business data DB to be applied to the corresponding watershed, the generated inflow data is used Calculating a storage amount according to a drought response criterion; (b) classifying the year in which the yearly classification module is in a serious stage in which the amount of water estimated in the water amount estimation module is less than a serious stage in which a drought lasts for a predetermined period; (c) calculating a drought probability through a frequency at which the drought probability calculation module falls below the critical stage, and calculating a drought damage amount and a drought reduction amount based on a frequency at which the drought damage calculation module falls below the critical stage; (d) The probability of each uncertainty of benefit (B) and cost (C) for each node from the estimation of drought probability, drought damage, and drought reduction according to frequency of decision tree construction module down to the above critical stage Multiplying each of them and calculating and inserting them and advancing and selecting the node with the highest value step by step as an option of Invest & Operation, Delay and Abort; (e) analyzing and outputting the result analysis module to a scenario set by using all possible combinations of decision trees according to the selected option, and outputting the analyzed result to a physician based on real option analysis in consideration of uncertainty of climate change And a method of constructing a crystal tree.

(여기서, S_t: t 시점에서의 저수량, I_t: t 동안의 유입량, R_t: t 동안의 방류량)으로부터 저수량을 산정할 수 있다.Further, in the present invention, in the step (a), the low water amount calculation module may calculate the low water amount,

(Where, S _t is a storage amount at time _t , I _t is an inflow amount during t, and R _t is a discharge amount during t).

(여기서, k: k번째 시나리오(k=1은 정상, k=2는 약한 가뭄, k=3은 극한 가뭄), n: 심각단계 이하로 내려간 연도의 개수, N: 총 연도)로부터 가뭄 확률을 산출하고, 상기 가뭄 피해액 산정모듈은 다음의 수학식,

(여기서, I_n: 실수요 공급량(정상상태에서의 공급량), I_d: 심각단계 이하 시 공급량, P_w: 용수 단가, D_k: k상태에서의 평균 심각단계 이하 일수)으로부터 가뭄 피해액을 산정할 수 있다.Also, in the present invention, in the step (c), the drought probability calculation module calculates the drought probability using the following equation,

Where k is the probability of drought from the kth scenario (where k = 1 is normal, k = 2 is a weak drought, k = 3 is an extreme drought), n is the number of years below the critical stage, The drought damage calculation module calculates the drought damage amount using the following equation,

(Where I _{n is the} actual supply (supply in the steady state), I _d is the supply under severe stage, P _{w is the} water price, and D _k is the number of days under the severe stage in k state) .

Further, in the present invention, in the step (c), the drought damage calculation module calculates the drought damage amount using the following equation,

(여기서, B_Project,k: 가뭄 저감액, C_d: 부족량을 채워주는 추가 공급량(투자사업에 의한 공급량), P_w: 용수 단가, D_k: k상태에서의 평균 심각단계 이하 일수)으로부터 가뭄 저감액을 산정할 수 있다.

(Where B _{project, k} : drought reduction, C _d : additional supply to fill the deficit, P _w : water unit price, D _k : The amount of reduction can be calculated.

Further, in the present invention, in the step (d), the decision tree construction module calculates the following equation

(여기서, x는 옵션(x=1: 투자와 운영, x=2: 연기, x=3 포기), t는 분석연도 차수, r은 할인율, k는 k번째 시나리오(k=1은 정상, k=2는 약한 가뭄, k=3은 극한 가뭄), B_t,x는 가뭄저감액, C_t,x는 가뭄피해액)으로부터 해당연도의 각 옵션에 따른 NPV값을 산출하고, 상기 (e) 단계에서, 결과 분석모듈이 분석기간 동안 상기 NPV값의 합이 가장 높은 옵션의 조합이 최적의 옵션 조합으로 평가한다.

(Where x is the option ( x = 1: investment and operation, x = 2: deferred, x = 3 giving up), t is the analytical year, r is the discount rate, k is the kth scenario (D) is the drought severity, (2) is the weak drought, (3) is the extreme drought), B _{t, x} is the drought reduction, C _{t and x} is the drought damage value) , The result analysis module evaluates the combination of the options with the highest sum of the NPV values during the analysis period as the optimal option combination.

According to the present invention, by using decision tree as a model for solving real options, it is possible to use more various options than other real option analysis models, to consider various uncertainties, Unlike existing methods that assess accurate economic value, determine the timing of an appropriate investment, and evaluate assumptions of normal climatic conditions, there is an advantage in assessing value in disasters such as drought.

1 is a block diagram illustrating an application for building a decision tree in a decision tree construction system based on real option analysis in consideration of uncertainty of climate change, according to an embodiment of the present invention.
2 is a flowchart illustrating a method for constructing a decision tree based on real option analysis in consideration of uncertainty of climate change according to the present invention.
FIG. 3 is a table showing the benefits and costs according to the option in the decision tree construction method based on the real option analysis in consideration of the uncertainty of the climate change according to the present invention.
FIG. 4 is a diagram illustrating a scenario using decision trees in a decision tree construction method based on real option analysis in consideration of uncertainty of climate change according to the present invention.
5 is a table showing a combination of all the options of the model in the decision tree construction method based on real option analysis in consideration of the uncertainty of climate change according to the present invention.
FIG. 6 is a table for analyzing the cost benefits according to the combination of options in the decision tree construction method based on the real option analysis in consideration of the uncertainty of the climate change according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of a decision tree construction method based on real option analysis will be described in detail with reference to the accompanying drawings, taking into consideration uncertainty of climate change according to the present invention.

First, the cash flow discount method is a theoretical background of the present invention. The cash flow discounting method is the method used to evaluate the investment opportunity (Invest Opportunity). This method predicts future cash flows and applies the discount rate accordingly to express the potential value as the present value. If the value obtained from this analysis is higher than the current investment cost, it can be judged that investment possibility exists. Three methods are used for the discounted cash flow method: Net Present Value (NPV), Profitability Index (PI) and Internal Rate of Return (IRR).

The net present value method is a method of converting the future net benefit to the present value by applying a discount rate. The net benefit here is the benefit minus the cost. This can be expressed as the value of the business being increased or decreased as the investment plan is adopted. If the net present value obtained through the above process is greater than 0, it is judged that the investment is valid. The net present value (NPV) is calculated by the following equation (1).

(Where N _t is the net present value of the year t, i is the discount rate, and t is the total analysis period)

While the net present value method can add up values when investing in several alternatives, the fluctuation of net present value due to discount rate can be somewhat large.

Next, real option analysis (ROA) is based on the concept of a financial option. Option is to sell an underlying asset with an Exercise Price predefined on the maturity date The option buyer has the right to buy. This real option analysis is an extension of the cash flow discount method, which is the traditional decision-making method presented above. In the case of the cash flow discounting method, cash flow over the lifetime of each alternative is estimated and the most economical alternative is selected. At this time, the selected alternative can not be changed to another car again during the proposed lifetime. However, in the real option analysis, the selected alternative can be changed through various options, and it can be watched and configured step by step because it is not a definite alternative. That is, it can be expressed as a valuation method considering flexibility.

An economic assessment based on real option analysis can be defined as an expanded net present value (ENPV) with flexibility. Flexible value may be viewed as a feasible solution if the real option analysis method is considered impractical for traditional economic analysis, which is called the option value or option premium. In other words, the value obtained by subtracting the static net present value from the expanded value is the option premium. The value of the option premium can be confirmed by the following Equation (2).

The method of confirming the timing of using the option considered above can be explained by the following example of Equation (3).

(Where D is the value of the deferral option)

If the net present value is greater than when the option is deferred, ENPV is the net present value. In the opposite case, however, the value of choosing the postponement option becomes ENPV . That is, at a certain point in time, when the options including the net present value are compared, it is a real option analysis to select the value having the highest value.

The basic options in the real option analysis are the Delay option first, the Expand or Reduction option, and finally the Abort or Switch option. These three options are called Simple Options. Growth, Shut Down, and Compound are also available.

The investor can choose to postpone the investment until there is additional information about the project, such as information on future market developments. Deferral options can represent great value for project uncertainty and irreversible projects. This option is particularly valuable in resource extraction projects, agricultural or real estate development. This is because uncertainty about long-term investment is very high. Next is the expand or collapse option. This allows the decision maker to make adjustments to the size of the project as it is invested in the project. For example, a company can acquire a competitor and expand its current business activities. Decision makers may also decide to reduce the size of the project if the outcome of the investment is less than expected. These two options provide an opportunity for decision makers to adapt to market volatility. Companies have the option to give up existing projects if the project situation is not good. This is called abandonment option. Often, companies minimize losses through this method.

Companies can also have the option to switch from one project to another. These options are called conversion options. Generally, companies abandon existing projects and proceed with new projects. Because it is very difficult to make a decision between two interdependent projects. For this reason, the conversion option is also called a complex option.

Over the years, various methods have been proposed to actually apply the real option analysis concept. Some have been applied from the field of economics, and others have emerged from decision theory. Therefore, it can be verified that the assumptions are various according to the problems dealt with in each field. Among the various methods, the decision tree model is adopted in the present invention among four most commonly used methods, namely, the Black-Scholes model, the binomial tree model, the simulation model, and the decision tree method.

The decision tree model has the advantage of being able to deal with more various types of options than the other models in real option analysis, and it can present a flexible strategy. It is also easy to understand or explain conceptually. However, implementation through computer programming is very complicated and can take a relatively long time to apply.

Also, in the present invention, a real option analysis model is presented by applying a decision tree having a wide range of application and high usefulness of results to domestic water resources projects.

In FIG. 1, the decision tree building application (1) based on real option analysis is a programmed tree structure that is programmed in a computer readable recording medium that can be operated in various computer systems such as a server, a desktop computer, will be.

In the application 1, the future inflow data generation module 10 generates a future inflow data from a future inflow data database of a corresponding dam or a watershed created by, for example, Water Resources Corporation. The reservoir estimating module 20 estimates the reservoir volume based on the drought response criterion for a predetermined period of time from the inflow data observed from the basin or dam from the data generated by the future inflow data generating module 10. The yearly classification module 30 is for classifying the years in which the amount of water estimated by the water amount estimation module 20 is below a serious stage in which a drought lasts for a predetermined period. The drought probability calculation module 40 calculates a drought probability through a frequency that falls below a serious stage and the drought damage calculation module 50 calculates a drought damage amount and a drought reduction amount through a frequency lower than a serious stage. In addition, the decision tree building module 60 multiplies the values of each node by the probability of drought, the amount of drought damage and the amount of drought reduction according to the frequency of descending below the critical stage, and multiplies it by the uncertainty probability of benefit and cost, The most valuable node is step by step, with the option of investment and operation, delay and abort. The result analysis module 70 analyzes and outputs the scenario according to the selected option using all possible combinations of decision trees.

FIG. 2 is a flow chart illustrating a procedure for applying a real option analysis to a method for constructing a decision tree based on real option analysis in consideration of the uncertainty of climate change according to the present invention.

First, the future inflow data generation module 10 collects and generates business data for application (S10). At this time, it is recommended that the data of the project is already constructed for a certain period of time. In other words, the storage capacity of the corresponding dam, for example, Boryeong Dam, is used to calculate the storage capacity (S20). Based on this, the year and the number of days below the critical stage of the Boryeong Dam drought standard are determined (S30), and the probability of drought and the amount of drought damage (including drought reduction) are respectively calculated (S40). Then, based on the alternative water resource project data, the value of the option is grasped and a decision tree is constructed (S50). In addition, uncertainty values are identified through cost-benefit analysis results in consideration of three climate scenarios: normal, weak drought, and extreme drought (S60). A real option analysis (ROA) will also be calculated as a result of using the option to defer and abandon and present the optimal plan for this project.

Hereinafter, a detailed example of the algorithm for constructing the decision trees will be described with reference to generation of 500-year inflow from the Boryung Dam observation inflow data data from 1998 to 2013.

Therefore, a total of 500 years of water storage was estimated using future inflow data. The following equation (4) is applied for the estimation of the storage capacity.

(Where, S _t is the storage amount at the time _t , I _t is the inflow amount during t, and R _t is the discharge amount during t)

The discharge rate is determined according to the Boryung Dam drought response standard. The amount of water is supplied until the stage of interest, and water is supplied from maintenance stage, agricultural water from boundary stage, and life and industrial water from severe stage.

And classify the years below the critical stage of the estimated reservoir data. In 2015, Boryeong Dam was defined as extreme drought when the water level dropped below the critical level for a total of 135 days, 135 days or less during the year, weak drought less than 135 days, Were classified as normal. During a total of 490 years (10 years out of 500 are excluded as a reference period), a weak drought occurred in 24 years and on average dropped below the critical stage of about 36 days. The extreme drought occurred 7 times and stayed below the serious stage on average 161 days.

The probability of drought is defined by the following equation (5).

(Where k = 1 is normal, k = 2 is a weak drought, k = 3 is an extreme drought), n is the number of years below the critical stage, and N is the total year.

The result of calculating the drought probability in the Boryeong Dam using Equation (5) is shown in Equation (6).

Therefore, the probability of the normal condition (Normal) was 0.94, the weak drought (WD) was 0.05, and the extreme drought was 0.01.

In addition, the calculation of the drought damage amount is calculated by the following Equation (7).

(Where I _{n is the} actual supply (supply in the steady state), I _d is the supply at the critical stage or less, P _{w is the} water price, and D _k is the number of days under the severe stage in the k state)

Options used in real option analysis (ROA) generally exist in a variety of ways. In the present invention, a total of three options are used to suit the characteristics of the application. The costs and benefits accruing to the options are shown in FIG. At Boryeong Dam, when the water level is below the critical stage, the water supply will be reduced by about 89,000 tons per day compared to the normal level. However, for example, in the case of irrigation (investment business), about 115,000 tons per day can be supplied to Boryeong Dam, which can reduce the damage caused by water loss. This is defined as the drought reduction. As shown in Equation (7), the drought reduction amount is calculated by the following Equation (8).

(Where B _{project, k is the} drought reduction, C _d is the additional supply that meets the deficit, and C _d is the deficiency if the supply by the investment project exceeds the deficiency)

In the case of the irrigation (investment) project, the irrigation cost will be the construction cost in Fig. 3, and the combined total of the operation cost based on the minimum operation cost and the water supply days after completion of irrigation will be the operation cost in Fig.

Next, referring to the table showing the benefits and costs per option in FIG. 3, the first option is Invest & Operation (I & O). If this option is selected, construction will be carried out before construction is completed, and construction costs will be incurred, and drought damage will occur depending on the scenario. After the construction is completed, drought reduction benefits will occur. In addition, if the cost of operation and the supply of water are insufficient, the amount of drought damage to the deficit will occur. The second option is Delay. If you choose the option to postpone, you will not proceed with the construction of the project, but will move on to the next year. If this option is selected, it means that the value of the deferred option is higher than the investment and operating option at that time. If you choose the option to defer, there will be no benefit and drought damage will occur. The last option is Abort. Option to abandon a business investment if it is deemed not worth the investment and operating option during the remaining analysis period after selecting the option to postpone.

Fig. 4 shows the decision tree constructed based on this. In FIG. 4, the symbol x denotes the case where the combination of options can not occur, and the value of each node is multiplied by the probability of uncertainty for each benefit and cost, and is calculated and inserted as shown in Equation (9). The value of each node during the analysis period is calculated and the node with the highest value in the step is advanced and selected.

(Where x is the option ( x = 1: investment and operation, x = 2: deferred, x = 3 giving up), t is the analytical year, r is the discount rate, k is the kth scenario = 2 is weak drought, k = 3 is extreme drought), B _{t, x} is drought reduction, C _{t, x} is drought damage)

In other words, the sum of the weighted probabilities is calculated by multiplying the difference between benefits and costs by the drought probabilities according to k and the respective analysis years. On the other hand, when the order of the analysis year elapses, operating expenses or water shortage in each year may be changed in cost.

Next, as a valuation based on the use of options, the results were confirmed by taking into consideration the options for delaying and abandoning the model. All possible combinations of decision trees are shown in FIG. 5, and the NPV values according to each option in the corresponding year are shown in FIG. Here, 30 years is an example of the period of the above-mentioned waterway project of Boryeong Dam, and 31 combinations show only when combination of options can occur.

The optimal option combination is the combination with the highest sum of the NPV values during the analysis period (for example, the irregular business period of 30 years), which can be regarded as having the highest economic value during the analysis period. Are the rightmost values.

While the invention has been shown and described with respect to the specific embodiments thereof, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined by the appended claims. Anyone with it will know easily.

1: Application 10: Future Inflow Data Generation Module 20: Capacity Calculation Module 30: Yearly Classification Module 40: Drought Probability Calculation Module 50: Drought Damage Estimation Module 60: Decision Tree Construction Module 70:

Claims (5)

(a) Future inflow data from the future inflow data generation module and the amount of discharge determined according to the drought countermeasure standard (water supply is supplied until the stage of interest, maintenance water is supplied from the state stage, Life and industrial water are supplied in a reduced amount), the low water amount calculating module calculates the water amount,
The storage amount calculation module calculates the storage amount

(Where S _t is a storage amount at time _t , I _t is an inflow amount during t, and R _t is a discharge amount during t);
(b) The year-by-year classification module classifies the years in which the water level estimated by the water level estimation module is below the severe stage where the drought lasts for a certain period of time, ;
(c) calculating the drought probability through the frequency at which the drought probability calculation module falls below the critical stage, calculating the drought damage amount and the drought reduction amount through the frequency at which the drought damage calculation module falls below the critical stage,
The drought probability calculation module calculates the drought probability using the following equation

Where k is the probability of drought from the kth scenario (where k = 1 is normal, k = 2 is a weak drought, k = 3 is an extreme drought), n is the number of years below the critical stage, Respectively,
The drought damage calculation module calculates the drought damage amount using the following equation

(Where I _{n is the} actual supply (supply in the steady state), I _d is the supply under the severe stage, P _{w is the} water price, and D _k is the number of days under the severe stage in k state) However,
The drought damage calculation module calculates the drought damage amount using the following equation

(Where B _{project, k} : drought reduction, C _d : additional supply to fill the deficit (supply by the investment project). If the supply by the investment project exceeds the deficiency, C _d only applies the deficiency, P _w : Water price, and D _k : the number of days below the mean severity level in the k state);
(d) The probability of each uncertainty of benefit (B) and cost (C) for each node from the estimation of drought probability, drought damage, and drought reduction according to frequency of decision tree construction module down to the above critical stage And multiply and insert each of them and advance the node that has the highest value among the NPV values according to each option of the corresponding year as an option of Invest & Operation, Delay and Abort. However,
The decision tree construction module may be implemented by the following equation

(Where x is the option ( x = 1: investment and operation, x = 2: deferred, x = 3 giving up), t is the analytical year, r is the discount rate, k is the kth scenario = 2 is a weak drought, k = 3 is an extreme drought), B _{t, x} is a drought reduction, C _{t, x} is a drought damage value);
(e) analyzing and outputting the result analysis module to a scenario set by using all possible combinations of decision trees according to the selected option, and outputting the analyzed result to a physician based on real option analysis in consideration of uncertainty of climate change How to build a crystal tree.
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