模糊环境下的期权定价模型及其在高速公路项目中的应用研究
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摘要
项目价值评估是一个非常重要且复杂的问题。在保留传统方法合理内核基础上建立起来的实物期权定价方法,由于受到众多不确定因素的困扰,进而导致其在实际应用中的限制颇多,最为人诟病的就是对于不确定问题的处理方式。因此,为有效刻画期权定价模型中的不确定性,论文对模糊环境下的期权定价问题进行了研究,提出了一些更加符合实际、更加符合人性决策方式的期权定价模型,并设计了相应的分析步骤和求解过程。论文主要研究内容及结论如下:
(1)在对期权定价理论进行了全面、系统的分类、归纳、整理的基础上,结合国内外学者已有的研究成果,从风险中性和标的资产收益波动性固定的假设着手,通过分析经典B-S和二叉树期权定价模型的应用误差,提出了传统实物期权定价方法在实际应用中的限制。
(2)构建了基于模糊集合的二叉树期权定价模型。采用模糊理论来衡量实务上期权分析的模糊性,将模糊的观念作用于不确定参数的确定上,包括无风险利率和标的资产报酬波动性,建立了一期模糊二叉树买入期权定价模型,在此基础上将模型扩展至二期和多期,并给出了详尽的分析步骤和推导过程。
(3)构建了基于模糊决策空间的B-S期权定价模型。投资者处理期权定价模型的实际情景是一个由模糊样本信息、模糊状态、模糊行动及最终得出的买入期权价格即模糊评价函数构成的决策空间,为此应用模糊理论及贝式定理来度量该模糊性,据以作为估计期权定价模型中相关变量期望值的依据,并藉以建立期权定价模型,以确定不确定性情况下的B-S期权定价问题。
(4)以高速公路项目为例,建立全新模糊二叉树期权定价模型进行实证分析。利用JS高速公路项目的实际数据验证结果表明,基于模糊数的二叉树定价方法基本能够排除不确定因素的影响,可以形成一个具有类似置信区间的模糊区间,投资者可通过不断调整高速公路未来收入变化的模糊数的左右边界等变量,逐步调整其对未来收入的变化预期,进而在此区间内合理估计高速公路项目投资价值。
Value assessment of project investment is a very important and complicated issue. The traditional theories and methods of investment such as Real Option Value have been accepted and adopted at present. However, as they are restrained by so many uncertain factors, these methods have their own limitations. The most criticized problem is how to deal with the uncertainty. Therefore, in order to define the uncertainty in the Option Pricing Model, this paper attempts to study the option pricing problems on the basis of fuzzy environment. And then it proposes some more practical and reasonable Option Pricing Model. In the end, corresponding analysis procedure and solving process are presented. The following is the main content and conclusion of the paper:
Firstly, after classifying, inducing and regulating the method of project investment & construction value and the theory of option pricing comprehensively and systematically, and combined with the former researches both at home and abroad, this paper starts with the hypothesis of neutral risk and fixed fluctuation of underlying assets and analyze the implementation error of classic B-S and B-tree option pricing models, then proposed the limitation of traditional real option pricing method in practical application.
Secondly, this paper builds up B-tree Option Pricing Model based on fuzzy set. In addition it builds up the First Phase Fuzzy B-tree Call Option Pricing Model by measuring the fuzziness of analysis on real option with the fuzzy theory, and utilizing the view of fuzziness to confirm the uncertain parameters including the risk-free rate of interest and the fluctuation of underlying asset remuneration. Then it expands the model to the second and multiple phase and presents the analysis procedure and deduction process in detail.
Thirdly, this research also builds up B-S Option Pricing Model based on fuzzy decision-making space. The process that investors deal with Option Pricing Model is actually a decision-making space composed of fuzzy sample information, fuzzy status, fuzzy action and the finally achieved call option price, i.e. fuzzy assessment function, therefore using fuzzy theory and Bayes’theorem to measure the fuzziness, hereby to assess the desired value of correlative variables in Option Pricing Models and build up Option Pricing Models to decide the B-S option pricing under uncertain circumstance.
Finally, a new Fuzzy B-tree Real Option Model is built to establish an empirical analysis, using an expressway project as an example. The empirical result of JS express highway project manifests that the B-tree pricing method based on fuzzy number is capable to avoid the influence of uncertain factors. Besides, a fuzzy interval similar to confidence interval is formed so that the investor can adjust his expectation on the change of the future income by constantly adjusting the variables such as fuzzy number’s border, etc., and then make a reasonable assessment on the investment value of the expressway in this interval.
(1)在对期权定价理论进行了全面、系统的分类、归纳、整理的基础上,结合国内外学者已有的研究成果,从风险中性和标的资产收益波动性固定的假设着手,通过分析经典B-S和二叉树期权定价模型的应用误差,提出了传统实物期权定价方法在实际应用中的限制。
(2)构建了基于模糊集合的二叉树期权定价模型。采用模糊理论来衡量实务上期权分析的模糊性,将模糊的观念作用于不确定参数的确定上,包括无风险利率和标的资产报酬波动性,建立了一期模糊二叉树买入期权定价模型,在此基础上将模型扩展至二期和多期,并给出了详尽的分析步骤和推导过程。
(3)构建了基于模糊决策空间的B-S期权定价模型。投资者处理期权定价模型的实际情景是一个由模糊样本信息、模糊状态、模糊行动及最终得出的买入期权价格即模糊评价函数构成的决策空间,为此应用模糊理论及贝式定理来度量该模糊性,据以作为估计期权定价模型中相关变量期望值的依据,并藉以建立期权定价模型,以确定不确定性情况下的B-S期权定价问题。
(4)以高速公路项目为例,建立全新模糊二叉树期权定价模型进行实证分析。利用JS高速公路项目的实际数据验证结果表明,基于模糊数的二叉树定价方法基本能够排除不确定因素的影响,可以形成一个具有类似置信区间的模糊区间,投资者可通过不断调整高速公路未来收入变化的模糊数的左右边界等变量,逐步调整其对未来收入的变化预期,进而在此区间内合理估计高速公路项目投资价值。
Value assessment of project investment is a very important and complicated issue. The traditional theories and methods of investment such as Real Option Value have been accepted and adopted at present. However, as they are restrained by so many uncertain factors, these methods have their own limitations. The most criticized problem is how to deal with the uncertainty. Therefore, in order to define the uncertainty in the Option Pricing Model, this paper attempts to study the option pricing problems on the basis of fuzzy environment. And then it proposes some more practical and reasonable Option Pricing Model. In the end, corresponding analysis procedure and solving process are presented. The following is the main content and conclusion of the paper:
Firstly, after classifying, inducing and regulating the method of project investment & construction value and the theory of option pricing comprehensively and systematically, and combined with the former researches both at home and abroad, this paper starts with the hypothesis of neutral risk and fixed fluctuation of underlying assets and analyze the implementation error of classic B-S and B-tree option pricing models, then proposed the limitation of traditional real option pricing method in practical application.
Secondly, this paper builds up B-tree Option Pricing Model based on fuzzy set. In addition it builds up the First Phase Fuzzy B-tree Call Option Pricing Model by measuring the fuzziness of analysis on real option with the fuzzy theory, and utilizing the view of fuzziness to confirm the uncertain parameters including the risk-free rate of interest and the fluctuation of underlying asset remuneration. Then it expands the model to the second and multiple phase and presents the analysis procedure and deduction process in detail.
Thirdly, this research also builds up B-S Option Pricing Model based on fuzzy decision-making space. The process that investors deal with Option Pricing Model is actually a decision-making space composed of fuzzy sample information, fuzzy status, fuzzy action and the finally achieved call option price, i.e. fuzzy assessment function, therefore using fuzzy theory and Bayes’theorem to measure the fuzziness, hereby to assess the desired value of correlative variables in Option Pricing Models and build up Option Pricing Models to decide the B-S option pricing under uncertain circumstance.
Finally, a new Fuzzy B-tree Real Option Model is built to establish an empirical analysis, using an expressway project as an example. The empirical result of JS express highway project manifests that the B-tree pricing method based on fuzzy number is capable to avoid the influence of uncertain factors. Besides, a fuzzy interval similar to confidence interval is formed so that the investor can adjust his expectation on the change of the future income by constantly adjusting the variables such as fuzzy number’s border, etc., and then make a reasonable assessment on the investment value of the expressway in this interval.
引文
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