不确定环境下期权定价模型及应用研究
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摘要
在金融市场中存在着大量的客观或主观的不确定性,如随机性、模糊性等。随着实证研究的不断深入,人们发现这种不确定性影响着决策者的行为选择进而影响着资产价的变化。人们越来越关注不确定性如何在模型中更好的体现出来,从而为决策提供有效的思路和方法。论文对不确定环境下的期权定价问题进行了研究,提出了一些更符合实际的期权定价模型,并设计了相应的求解算法。主要研究内容如下:
讨论了已有的期权定价模型,对国内外研究状况进行了详细的分析比较,分别指出了优缺点和可改进之处。
研究了波动率为模糊变量的情况,分别建立了离散和连续模糊波率期权定价模型,给出了模糊欧式买权和卖权的对称定价公式。根据模糊模拟技术设计了估算期权价值的算法,结合实例说明方法的应用。
研究了证券未来价值的不确定性,采用可信性理论来表示投资者对标的证券价格的主观推断与权衡,用模糊过程表示证券未来价值的不确定性,建立了离散时间和连续时间美式期权定价模型,并对不付红利股票美式看涨、看跌期权定价分别进行了分析,通过数值算例进行了验证。
研究了股票价格服从跳扩散过程的情况,把跳跃强度描述为模糊变量,建立了股票价格为随机模糊跳-扩散过程期权定价模型。并设计了估算期权价值的智能算法,通过数值算例进行了求解和分析,结果表明了模型和算法的有效性。
根据可信性理论提出了一种新的模糊过程,证明了其理论上的正确性,用模糊微分方程来描述原生资产价格演化过程,建立了模糊过程期权定价模型。
研究了股票期权定价中的不确定性因素,考虑了传统欧式期权定价模型中存在的定价偏差,在经典期权定价模型的基础上,假定股票价格是模糊随机过程。建立了模糊随机欧式期权定价模型,推导了期权的模糊定价公式。将提出的模型应用到权证定价,在权证定价时选取中国证券市场的实际数据检验可信性理论的实用性及其输入变量的经济含义。与传统的Black-Scholes公式的结果进行比较,并对期权价格偏离B-S理论定价给出解释。
In the real financial market, there are always other uncertain phenomena,such as fuzzy phenomenon, random phenomenon. Along with empirical studyincreasing investigator discovered that this kind of uncertainty a?ects policy-maker’s behavior choice and the asset price change. Researcher pay more andmore attention to the problems on the option pricing under in uncertain environ-ments, Therefore, the dissertation shows that options can be valued successfullyin uncertain environments, some option pricing models are established, the corre-sponding algorithm is designed to solve these models. The contents are describedas follows:
We discuss the existing option pricing model, and carry out a detailed anal-ysis and comparison. Then point out theirs advantages, disadvantages and im-provements.
The fuzzy volatility pricing option models are proposed, in which the volatil-ity is depicted as a continuous and discrete fuzzy variable. Then we discuss themethods how to derive the expected value of fuzzy option price. In addition,fuzzy simulation techniques are designed to estimate the value of option. Finally,a numerical example is given to demonstrate the idea in the models.
By considering the investor’s subjective factors in process to infer Americanput option price, the fuzzy American option pricing model of discrete time andcontinues-time are established, respectively. in which the price of stocks is takenas fuzzy variables. Moreover, the expected value of option price is derived by themaking-decision attitude.
A random fuzzy jump-di?usion option pricing model is proposed, where thevolatility and the jumps intensity are depicted as fuzzy variables, respectively.As a sequence, the European option price turns into the fuzzy variable. Fuzzysimulation technique is designed to estimate the membership degree and theexpected value of the option. The rough figures of the expected value of optioncan be obtained.
Fuzzy L process is proposed by the credibility theory with accuracy theoret-ically proof. An option valuation model using fuzzy L process is constructed. Wedemonstrate how fuzzy L process can be successfully applied to the risk neutraloption pricing model with applying fuzzy calculus to finance.
The paper presents the fuzzy random option pricing models for Europeanoption, in which the evolution of stocks price are taken as fuzzy random process.Moreover, in order to make-decision better for the investor, the expected valueof option price can be derived by the formula. We apply fuzzy random optionpricing models to warrant pricing with the empirical analysis by the Chinesesecurities historical data, and explode the input variable economical meaning.We compare the proposing model with traditional Black-Scholes model. Keywords: Uncertainty, Fuzzy theory, Option pricing model, Empirical analysis
讨论了已有的期权定价模型,对国内外研究状况进行了详细的分析比较,分别指出了优缺点和可改进之处。
研究了波动率为模糊变量的情况,分别建立了离散和连续模糊波率期权定价模型,给出了模糊欧式买权和卖权的对称定价公式。根据模糊模拟技术设计了估算期权价值的算法,结合实例说明方法的应用。
研究了证券未来价值的不确定性,采用可信性理论来表示投资者对标的证券价格的主观推断与权衡,用模糊过程表示证券未来价值的不确定性,建立了离散时间和连续时间美式期权定价模型,并对不付红利股票美式看涨、看跌期权定价分别进行了分析,通过数值算例进行了验证。
研究了股票价格服从跳扩散过程的情况,把跳跃强度描述为模糊变量,建立了股票价格为随机模糊跳-扩散过程期权定价模型。并设计了估算期权价值的智能算法,通过数值算例进行了求解和分析,结果表明了模型和算法的有效性。
根据可信性理论提出了一种新的模糊过程,证明了其理论上的正确性,用模糊微分方程来描述原生资产价格演化过程,建立了模糊过程期权定价模型。
研究了股票期权定价中的不确定性因素,考虑了传统欧式期权定价模型中存在的定价偏差,在经典期权定价模型的基础上,假定股票价格是模糊随机过程。建立了模糊随机欧式期权定价模型,推导了期权的模糊定价公式。将提出的模型应用到权证定价,在权证定价时选取中国证券市场的实际数据检验可信性理论的实用性及其输入变量的经济含义。与传统的Black-Scholes公式的结果进行比较,并对期权价格偏离B-S理论定价给出解释。
In the real financial market, there are always other uncertain phenomena,such as fuzzy phenomenon, random phenomenon. Along with empirical studyincreasing investigator discovered that this kind of uncertainty a?ects policy-maker’s behavior choice and the asset price change. Researcher pay more andmore attention to the problems on the option pricing under in uncertain environ-ments, Therefore, the dissertation shows that options can be valued successfullyin uncertain environments, some option pricing models are established, the corre-sponding algorithm is designed to solve these models. The contents are describedas follows:
We discuss the existing option pricing model, and carry out a detailed anal-ysis and comparison. Then point out theirs advantages, disadvantages and im-provements.
The fuzzy volatility pricing option models are proposed, in which the volatil-ity is depicted as a continuous and discrete fuzzy variable. Then we discuss themethods how to derive the expected value of fuzzy option price. In addition,fuzzy simulation techniques are designed to estimate the value of option. Finally,a numerical example is given to demonstrate the idea in the models.
By considering the investor’s subjective factors in process to infer Americanput option price, the fuzzy American option pricing model of discrete time andcontinues-time are established, respectively. in which the price of stocks is takenas fuzzy variables. Moreover, the expected value of option price is derived by themaking-decision attitude.
A random fuzzy jump-di?usion option pricing model is proposed, where thevolatility and the jumps intensity are depicted as fuzzy variables, respectively.As a sequence, the European option price turns into the fuzzy variable. Fuzzysimulation technique is designed to estimate the membership degree and theexpected value of the option. The rough figures of the expected value of optioncan be obtained.
Fuzzy L process is proposed by the credibility theory with accuracy theoret-ically proof. An option valuation model using fuzzy L process is constructed. Wedemonstrate how fuzzy L process can be successfully applied to the risk neutraloption pricing model with applying fuzzy calculus to finance.
The paper presents the fuzzy random option pricing models for Europeanoption, in which the evolution of stocks price are taken as fuzzy random process.Moreover, in order to make-decision better for the investor, the expected valueof option price can be derived by the formula. We apply fuzzy random optionpricing models to warrant pricing with the empirical analysis by the Chinesesecurities historical data, and explode the input variable economical meaning.We compare the proposing model with traditional Black-Scholes model. Keywords: Uncertainty, Fuzzy theory, Option pricing model, Empirical analysis
引文
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