基于实物期权理论的项目投资决策方法研究
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摘要
随着技术更新的加快和市场竞争的加剧,企业发展面临着越来越大的不确定性,这使得投资决策要承担更大的风险。如何控制风险和正确评估投资项目的价值,成为当代企业进行投资决策所面临的一个日趋重要的课题。传统的投资评估方法只是从静态角度考虑投资面临的风险,往往忽视管理者在整个过程中的灵活性,如放弃、转换、扩大投资等,因此不能准确评估投资项目的价值,从而导致投资决策的失误。将期权思想引入到投资决策领域,把投资中存在的选择权视为一种期权,就形成了实物期权概念。利用实物期权的观点看待投资,可以更好地理解不确定性、风险、收益三者之间的关系。实物期权理论将投资项目中的各种投资机会与经营柔性视作期权进行量化分析研究,充分考虑了投资活动中各种灵活性的价值,是投资决策理论的一项重要创新。
本文基于实物期权理论,将项目投资决策划分为单项目投资决策和项目组合投资决策,从这两个角度对项目投资决策方法进行了研究,本文主要做了如下工作：
(1)提出了一种新型模糊实物期权定价方法。通过利用模糊集理论,使用正态模糊数表示预期现金流收益现值,并提出利用格贴近度构造权向量,构造出一种新型实物期权定价方法。该方法考虑了投资者在模糊环境下进行的投资决策中许多数据不能精确量化的事实,借助模糊集理论提高定价方法的实际应用价值。此外,经证明发现用正态模糊数表示预期现金流收益更为合理,从而通过构造新型模糊实物期权方法为单项目投资决策提供理论依据。
(2)针对大多数项目投资具有时间选择的特性,提出一种基于美式实物期权的项目投资决策分析方法。该法主要针对美式期权定价模型的抛物型方程自由边值问题构造出一种变网格差分方法,它有两个优点：一是求解区域限定在自由边界内,从而减少了计算量；二是在求出期权值的同时也求出了期权的最佳执行边界。该方法能够为项目投资的实物期权提供理论求解方法,同时能够确定项目的最佳投资时间,为投资者是否进行项目投资提供决策,理论和实验显示该方法是高效而准确的。此外,本文结合实际项目投资决策的具体过程详细分析了基于美式实物期权的项目投资决策方法,使得管理者更为直观地掌握基于实物期权的项目投资决策方法,为企业进行项目投资决策提供理论和实践指导。
(3)针对项目组合选择问题的高效性、战略性及实时性,建立了基于实物期权理论的项目组合选择决策系统。在该决策系统中,从企业战略角度筛选备选项目,缩小备选项目集,以提高项目组合选择决策运算和求解效率。通过结合模糊实物期权理论及模糊净现值方法定义一种模糊评价函数。运用这个评价函数,可以为投资项目排序并且得到每个项目的最佳投资时间,最终可以得到满足所有给定约束的项目组合。在这个决策系统中,我们提出一种实时校正过程来随时更新项目组合,从而实现了对项目组合的动态管理。
(4)在项目组合选择问题中考虑资源约束并对资源进行合理调度能够使项目组合发挥出最大效用,基于这种想法我们建立了考虑资源合理调度的R&D项目组合选择模型。该模型应用模糊集理论和受限启发调度方法从大量的项目中选择出一组满足成本、资源及时间限制等条件并且使研发单位获得理想收益的项目组合。由于它考虑到资源的合理调度问题,尤其是我们对模型中可调度的资源进行抽象表示,在具体应用中,决策者可以根据企业实际情况,利用本模型选取人力资源、技术资源、财力资源或物资资源等进行调度,从而得到适合企业实际情况的优化调度模型。
(5)建立了不确定条件下考虑项目间相互影响的R&D项目组合选择模型。项目组合选择方法的实用性是项目组合选择理论研究中一个亟待解决的问题。也正是针对这一点,本文讨论如何从企业战略角度筛选备选项目,利用模糊集合理论处理相关不确定信息,通过在目标函数中添加项目的实物期权项来反映由项目管理决策的灵活性所带来的价值,通过定性和定量相结合的方法建立一种考虑项目间收益、技术以及资源相互影响关系同时发生的R&D项目组合选择模型。
总之,本文对基于实物期权的项目投资决策方法进行了深入研究,针对单项目与项目组合投资问题提出了决策方法。理论分析表明这些决策方法能够有效地为项目投资决策提供保证,实例模拟实验也证明了决策方法的有效性。
With the rapid technology innovations and severe competitions, business enterprises are facing more and more uncertainties. Consequently, investment projects have to bear more risk. How to control risks and assess correctly the value of investment projects has become an increasingly important topic in the contemporary corporate investment decisions. Traditional methods of investment appraisal is only from a static point of view of investment risks are often overlooked in the whole process managers flexibility, such as abandonment, conversion, expansion of investment and therefore they could not accurately assess the value of investment projects, resulting in investment decisions mistakes. Options thought introduced into the investment decision-making areas and the investment choice right to exist as a form of options lead to form a concept-real options. Use of real options view of investment can be a better understanding for uncertainties, risks, and benefits. Real options theory will view a variety of investment opportunities and management of flexible as options and make a quantitative analysis, which give full consideration to all kinds of flexibility values in investment activities. Real options theory is an important innovation of investment decision-making theory and method.
In this dissertation, we divide investment decision-making into single-project and project portfolio investment decision-making based on real option theory. Both from the perspective of the project investment decision-making methods have been studied. The main jobs have been done as following:
(1) A novel fuzzy real option pricing method has been presented. Through using fuzzy set theory, the use of normal fuzzy number is expected to express the present value of cash flow, and we make use of lattice closeness degree to construct weighted vectors. At last, we construct a new type of real option pricing method. This method considers the fact that many data cannot be accurately quantified when investors make investment decision in fuzzy environment. Using fuzzy set theory can improve the practical application value of investment decision-making method. In additional, we found it is logical to use a normal fuzzy number to predict the present value of expected payoff. So this new type of fuzzy real options approach can provide a theoretical basis for single-project investment decision-making.
(2) A project investment decision-making method has been proposed based on American real options owing to the timing characteristic of most of projects. In this dissertation, we construct a variable grid finite difference method about the parabolic equation free boundary value problem of American option pricing model. This method has two advantages:first, the computation can be reduced because of solution region limited in the free boundary; second, the option value and the best exercise boundary can be got together. Therefore, it provides a theoretical solution for real options included in project investment. At the same time, this method can also determine the optimal investment time for investors whether or not to conduct the project investment decision-making. Theory and experiment showed that the method is efficient and accurate. In addition, this paper displays visually actual project investment decision-making process, which can provide theory and practice guidance for enterprise project investment decision-making.
(3) Due to efficience, strategic and real-time of project portfolio selection, we set up a projects portfolio selection decision-making system based on real options theory. In this decision-making system, we screen chosen projects according to corporate strategy, which can narrow the set of alternative projects and improve efficiencies of project portfolio selection and computing. In additional, we define a fuzzy evaluation function through a combination of fuzzy real option theory and fuzzy net present value method. The use of the evaluation function, we can sort projects and get the optimal investment time of each project, and can eventually be bound to meet the entire given portfolio. In particular, in the decision-making system, we propose a real-time correction process to update the project portfolio, which will be the implementation of a dynamic project portfolio management.
(4) To consider the resource-constrained and resources scheduled reasonably can make project portfolio play a most effective. Based on this opinion, we construct an R&D projects portfolio selection model concerning resource scheduling. The model use fuzzy set theory and constrained scheduling method from many projects to meet the selection of a group of costs, resources and time constraints and make enterprise earning a better benefit. Because it takes into account the resource-scheduling problem, in particular, we make a abstract expression about resource scheduling in the model, which makes enterprise decision makers schedule the resources as human resources, technical resources, financial resources or material resources and so on in specific applications. Finally enterprises will get an optimal scheduling model fitting its actual situation.
(5) We proposed an R&D project portfolio selection model under uncertainty conditions concerning project interactions. The practicality of project portfolio selection methods is an issue in the project portfolio selection theory study. It is also aimed at this point to discuss how this article from the perspective of corporate strategy selection of alternative projects, the use of fuzzy set theory to deal with the related uncertainty information, the objective function by adding items of real options to reflect the value from project management flexibility, through combining qualitative and quantitative method to set up a R&D project portfolio selection model concerning projects interactions-benefits, technologies, and resources.
In short, this dissertation has studied project investment decision-making methods based on real options for single-project and project portfolio investment issues. Theoretical analysis shows that these decision-making methods can effectively provide guarantees for the project investment decision-making. In final, examples of simulation experiment prove the decision-making methods are effective.
本文基于实物期权理论,将项目投资决策划分为单项目投资决策和项目组合投资决策,从这两个角度对项目投资决策方法进行了研究,本文主要做了如下工作：
(1)提出了一种新型模糊实物期权定价方法。通过利用模糊集理论,使用正态模糊数表示预期现金流收益现值,并提出利用格贴近度构造权向量,构造出一种新型实物期权定价方法。该方法考虑了投资者在模糊环境下进行的投资决策中许多数据不能精确量化的事实,借助模糊集理论提高定价方法的实际应用价值。此外,经证明发现用正态模糊数表示预期现金流收益更为合理,从而通过构造新型模糊实物期权方法为单项目投资决策提供理论依据。
(2)针对大多数项目投资具有时间选择的特性,提出一种基于美式实物期权的项目投资决策分析方法。该法主要针对美式期权定价模型的抛物型方程自由边值问题构造出一种变网格差分方法,它有两个优点：一是求解区域限定在自由边界内,从而减少了计算量；二是在求出期权值的同时也求出了期权的最佳执行边界。该方法能够为项目投资的实物期权提供理论求解方法,同时能够确定项目的最佳投资时间,为投资者是否进行项目投资提供决策,理论和实验显示该方法是高效而准确的。此外,本文结合实际项目投资决策的具体过程详细分析了基于美式实物期权的项目投资决策方法,使得管理者更为直观地掌握基于实物期权的项目投资决策方法,为企业进行项目投资决策提供理论和实践指导。
(3)针对项目组合选择问题的高效性、战略性及实时性,建立了基于实物期权理论的项目组合选择决策系统。在该决策系统中,从企业战略角度筛选备选项目,缩小备选项目集,以提高项目组合选择决策运算和求解效率。通过结合模糊实物期权理论及模糊净现值方法定义一种模糊评价函数。运用这个评价函数,可以为投资项目排序并且得到每个项目的最佳投资时间,最终可以得到满足所有给定约束的项目组合。在这个决策系统中,我们提出一种实时校正过程来随时更新项目组合,从而实现了对项目组合的动态管理。
(4)在项目组合选择问题中考虑资源约束并对资源进行合理调度能够使项目组合发挥出最大效用,基于这种想法我们建立了考虑资源合理调度的R&D项目组合选择模型。该模型应用模糊集理论和受限启发调度方法从大量的项目中选择出一组满足成本、资源及时间限制等条件并且使研发单位获得理想收益的项目组合。由于它考虑到资源的合理调度问题,尤其是我们对模型中可调度的资源进行抽象表示,在具体应用中,决策者可以根据企业实际情况,利用本模型选取人力资源、技术资源、财力资源或物资资源等进行调度,从而得到适合企业实际情况的优化调度模型。
(5)建立了不确定条件下考虑项目间相互影响的R&D项目组合选择模型。项目组合选择方法的实用性是项目组合选择理论研究中一个亟待解决的问题。也正是针对这一点,本文讨论如何从企业战略角度筛选备选项目,利用模糊集合理论处理相关不确定信息,通过在目标函数中添加项目的实物期权项来反映由项目管理决策的灵活性所带来的价值,通过定性和定量相结合的方法建立一种考虑项目间收益、技术以及资源相互影响关系同时发生的R&D项目组合选择模型。
总之,本文对基于实物期权的项目投资决策方法进行了深入研究,针对单项目与项目组合投资问题提出了决策方法。理论分析表明这些决策方法能够有效地为项目投资决策提供保证,实例模拟实验也证明了决策方法的有效性。
With the rapid technology innovations and severe competitions, business enterprises are facing more and more uncertainties. Consequently, investment projects have to bear more risk. How to control risks and assess correctly the value of investment projects has become an increasingly important topic in the contemporary corporate investment decisions. Traditional methods of investment appraisal is only from a static point of view of investment risks are often overlooked in the whole process managers flexibility, such as abandonment, conversion, expansion of investment and therefore they could not accurately assess the value of investment projects, resulting in investment decisions mistakes. Options thought introduced into the investment decision-making areas and the investment choice right to exist as a form of options lead to form a concept-real options. Use of real options view of investment can be a better understanding for uncertainties, risks, and benefits. Real options theory will view a variety of investment opportunities and management of flexible as options and make a quantitative analysis, which give full consideration to all kinds of flexibility values in investment activities. Real options theory is an important innovation of investment decision-making theory and method.
In this dissertation, we divide investment decision-making into single-project and project portfolio investment decision-making based on real option theory. Both from the perspective of the project investment decision-making methods have been studied. The main jobs have been done as following:
(1) A novel fuzzy real option pricing method has been presented. Through using fuzzy set theory, the use of normal fuzzy number is expected to express the present value of cash flow, and we make use of lattice closeness degree to construct weighted vectors. At last, we construct a new type of real option pricing method. This method considers the fact that many data cannot be accurately quantified when investors make investment decision in fuzzy environment. Using fuzzy set theory can improve the practical application value of investment decision-making method. In additional, we found it is logical to use a normal fuzzy number to predict the present value of expected payoff. So this new type of fuzzy real options approach can provide a theoretical basis for single-project investment decision-making.
(2) A project investment decision-making method has been proposed based on American real options owing to the timing characteristic of most of projects. In this dissertation, we construct a variable grid finite difference method about the parabolic equation free boundary value problem of American option pricing model. This method has two advantages:first, the computation can be reduced because of solution region limited in the free boundary; second, the option value and the best exercise boundary can be got together. Therefore, it provides a theoretical solution for real options included in project investment. At the same time, this method can also determine the optimal investment time for investors whether or not to conduct the project investment decision-making. Theory and experiment showed that the method is efficient and accurate. In addition, this paper displays visually actual project investment decision-making process, which can provide theory and practice guidance for enterprise project investment decision-making.
(3) Due to efficience, strategic and real-time of project portfolio selection, we set up a projects portfolio selection decision-making system based on real options theory. In this decision-making system, we screen chosen projects according to corporate strategy, which can narrow the set of alternative projects and improve efficiencies of project portfolio selection and computing. In additional, we define a fuzzy evaluation function through a combination of fuzzy real option theory and fuzzy net present value method. The use of the evaluation function, we can sort projects and get the optimal investment time of each project, and can eventually be bound to meet the entire given portfolio. In particular, in the decision-making system, we propose a real-time correction process to update the project portfolio, which will be the implementation of a dynamic project portfolio management.
(4) To consider the resource-constrained and resources scheduled reasonably can make project portfolio play a most effective. Based on this opinion, we construct an R&D projects portfolio selection model concerning resource scheduling. The model use fuzzy set theory and constrained scheduling method from many projects to meet the selection of a group of costs, resources and time constraints and make enterprise earning a better benefit. Because it takes into account the resource-scheduling problem, in particular, we make a abstract expression about resource scheduling in the model, which makes enterprise decision makers schedule the resources as human resources, technical resources, financial resources or material resources and so on in specific applications. Finally enterprises will get an optimal scheduling model fitting its actual situation.
(5) We proposed an R&D project portfolio selection model under uncertainty conditions concerning project interactions. The practicality of project portfolio selection methods is an issue in the project portfolio selection theory study. It is also aimed at this point to discuss how this article from the perspective of corporate strategy selection of alternative projects, the use of fuzzy set theory to deal with the related uncertainty information, the objective function by adding items of real options to reflect the value from project management flexibility, through combining qualitative and quantitative method to set up a R&D project portfolio selection model concerning projects interactions-benefits, technologies, and resources.
In short, this dissertation has studied project investment decision-making methods based on real options for single-project and project portfolio investment issues. Theoretical analysis shows that these decision-making methods can effectively provide guarantees for the project investment decision-making. In final, examples of simulation experiment prove the decision-making methods are effective.
引文
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41.杜先进,孙树栋,欧立雄.多阶段R&D项目平衡组合选择模式研究[J],科学与科学技术管理,2006,27(11)：41-44.
42.欧立雄,余文明.企业项目化管理中战略层次的项目组合选择模型[J],科学技术与工程,2007,7(9)：2182-2185.
43.杨青,钟守楠,丁圣超.投资项目评价选择模型的遗传算法[J],运筹与管理,2006,15(1)：9-12.
44.张子力.基于遗传算法的工程项目投资方案优选模型[J],武汉大学学报,2004,37(6)：44-47.
45.周洪涛,王宗军,宋海刚.基于模糊优化的多目标投资组合选择模型研究[J],华中科技大学学报,2005,33(1)：108-110.
46.杜先进,孙树栋,欧立雄.基于相互影响的R&D项目组合选择[J],工业工程,2007,10(2)：130-133.
47.约翰·C·赫尔著；张陶伟译.期货期权入门(第三版)[M],北京：中国人民大学出版社,2000.
48. Myers S C. Finance Theory and Financial Strategy [J], Mildland Corporate Finance Journal,1977,5(1):6-13.
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50. Amram M, Kulatilaka N. Real options:managing strategic investment in an uncertain world [M], Boston:Harvard Business School Press,1999.
51.杨春鹏.实物期权及其应用[M],上海：复旦大学出版社,2003：1-10.
52. Cox J C, Ingersoll J E and Ross S A. A theory of the term structure of interest rates [J], Econometrica,1985,53(2):385-407.
53. Hull J. Options, Futures and Other Derivatives (Fourth Edition) [M], Englewood Cliffs, NJ:Prentice-Hall,2000.
54. Brennan M J, Schwarts E S. Evaluating natural resource investment [J], Journal of Business,1985,58 (2):135-157.
55. Paddock J, Siegel D and Smith J. Options valuation of claims on physical assets:the case of offshore petroleum lease [J], Quarterly Journal of Economics,1988,103 (3):479-508.
56. Trigeorgis L. Real Options:Managerial Flexibility and Strategy in Resource Allocation [M], Boston:MIT Press,1996.
57. Morck R, Schwartz E and Stangeland D. The valuation of forestry resources under stochastic prices and inventories [J], Journal of Financial and Quantitative Analysis,1989, 24:473-487.
58. Miles J A. Growth options and the real determinants of systematic risk [J], Journal of Business Finance & Accounting,1986,13(1):95-105.
59. Kellogg D, Charles J M, Real options valuation for a biotechnology company [J], Financial Analyst Journal,2000,56(3):76-84.
60. Schwartz E, Moon M. Rational pricing of internet companies [J], Financial Analyst Journal,2000,56:62-75.
61. Lenos T. Real options and interactions with financial flexibility [J], Financial Management,1993,22(3):202-218.
62. Dubois R. The optimality of multistage venture capital financing:An optiontheoretic approach [A], FMA European Conference, University of Siena Italy,2005.
63.赵秀云、李敏强.风险项目投资决策与实物期权估价方法[J],系统工程学报,2000,9.
64. Grenadier S R, Weiss A M. Investment in technological innovations:An option pricing approach [J], Journal of Financial Economics,1997,44(3):397-416.
65. Childs P D, Triantis A J, Dynamic R&D investment policies [J], Management Science, 1999,45(10):1359-1378.
66. Lambrecht B, Perraudin W, Real options and preemption under incomplete information [J], Journal of Economic Dynamics & Control,2003,27:619-643.
67.乔纳森·芒著；邱雅丽译.实物期权分析[M],北京：中国人民大学出版社,2006.
68.高建,周游,郑敬辉.技术价格评估中实物期权的应用[J],商业时代,2005(8)：85-91.
69.祝建民.期权定价中的波动率估计[J],统计与决策,2005(9)：127-129.
70. Baldwin C, Rruback. Inflation, Uncertainty and Investment [J], Journal of Finance,1986, 41(7):657-669.
71.肖翔.实物期权法在高新技术价值评估中的应用[J],北京交通大学学报(社会科学版),2007,6(2)：28-31.
72.陈永庆,王浣尘.期权理念在风险投资决策中的应用[J],管理工程学报,2001,15(2)：67-69.
73.吉兴全,文福拴.发电投资的实物期权决策方法[J],电力系统自动化,2005,29(11)：1-5.
74. Kong J J, Kwok Y K. Real optionsin strategic investment games between two asymmetric firms [J], European Journal of Operational Research,2007,181:967-985.
75. Chorn L G, Shokhor S. Real options for risk management in petroleum development investments [J], Energy Economics,2006,28:489-505.
76. Carlsson C, Fuller R. A fuzzy approach to real option valuation [J], Fuzzy Sets and Systems,2003,139(2):297-312.
77. Wang J, Hwang W L. A fuzzy set approach for R&D portfolio selection using a real options valuation model [J], Omega,2007,35(3):247-257.
78. Carlsson C, Fuller R. A fuzzy approach to R&D project portfolio selection [J], International Journal of Approximate Reasoning,2007,44(2):93-105.
79. Chen T, Zhang J L. A fuzzy group decision approach to real option valuation[C], Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg:2007,103-110.
80. Zadeh L A. Fussy Sets [J]. Information and Control,1965,8(3):338-353.
81. Wu H C. Pricing European options based on the fuzzy pattern of Black-Scholes formula [J], Computer & Operations Research,2004,31(7):1069-1081.
82. Benaroch M, Kauffman R J. Justifying electronic banking network expansion using real options analysis [J], MIS Quarterly,2000,24(2):197-225.
83. Dixit A K, Pindyck R S. The options approach to capital investment [J], Harvard Business Review,1995,62:56-68.
84. Broadie M, Detemple J. American option valuation:new bounds, approximations, and a comparison of existing methods [J], Review of Financial Studies,1996,9(4):1211-1250.
85. Allegretto W, Barone-Adesi G and Elliott R J. Numerical evaluation of the critical price and American options [J], European Journal of Finance,1995, (1):69-78.
86. Amin K, Khanna A. Convergence of American option values from discrete to continuous time financial models [J], Mathematical Finance,1994,4(4):289-304.
87.张铁.美式期权定价问题的数值方法[J],应用数学学报,2002,25(1)：113-122.
88. Mckean H P. A free boundary problem for the heat equation arising from a problem in mathematical economics [J], Industrial Management Review,1965,6(2):32-39.
89. Kwork Y K. Mathematical Models of Financial Derivatives [M], Berlin:Springer-Verlag, 1998.
90. http://www.pbc.gov.cn/detail.asp?col=460.
91. http://stock.homeway.com.cn/
92.范存彦,黄凯论.战略管理与项目管理的关联[J],美中经济评论,2004(3)：35-41.
93. Markowitz, Harry M. Portfolio Selection [J], The Journal of Finance,1952,7(1):77-91.
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98. Danneels E, Kleinschmidt E J. Product innovativeness from the firm's perspective:its dimensions and their relation with project selection and performance [J], The Journal of Product Innovation Management,2001,18(6):357-373.
99.丁宁.企业战略管理[M],北京：清华大学出版社,2005.
100.刘英骥.战略管理[M],经济管理出版社,2006.
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