基于模糊环境对回望期权定价问题的研究

发布时间：2018-03-30 20:13

本文选题：Black-Scholes公式　切入点：回望期权　出处：《吉林大学》2017年硕士论文

【摘要】：随着“中国经济新常态”的提出,金融市场将面临一个新的机遇和挑战.作为中国金融市场上的短板,金融衍生品的发展对于稳定金融市场运行、扩展金融市场都是至关重要的,更会关系到于实体经济的风险管理.自从1973年4月初,第一次在芝加哥期权交易所开始交易期权以来,我们发现期权市场的发展势头十分高歌猛进.在期权合约中,我们可以明显知道,期权价格——是唯一一个会随市场“供求关系”波动变化的自变量.因此,期权的价格会直接影响在合约中买卖双方的收益情况,这也导致期权定价问题成为了金融衍生品市场中最核心的问题.近年来,在国内外的金融衍生品交易市场的交易合约中,除了我们最熟悉的欧式期权、美式期权这些普通期权之外,还活跃着大量由标准期权派生出的更为个性化的奇异期权.它们的产生,是衍生品设计者为满足投资者更加个性化的投资偏好,迎合市场需求构造出的新组合.回期期权就是新型期权中备受欢迎的一种.由于最大收益可能且遗憾最小的特点,回望期权的价格也就变得相对贵一些,所以如何更准确地对回望期权进行定价,这是一个具有重大意义的研究方向.随着我们对期权定价问题的深入研究很容易发现,期权价格所依赖的金融环境,非常复杂且具有模糊性.这其中包含着主观和客观两方面的影响因素:主观上,受投资者的风险偏好影响,不一而足;客观上,受政策及市场等非随机不确定性影响.虽然主观因素无法避免,但是为了处理这些可解决的客观上的非随机不确定性,我们可以在期权定价的模型中,引入模糊数学理论.这也是最近几年才涌现的金融领域中的一个新的方向.本文基于传统的Black-Scholes期权定价模型[2],通过总结升华国内外知名学者的研究经验,决定尝试以三角模糊数和扩张原理等工具,创新性地把模糊数学理论引入到回望期权的定价中,得到回望期权的模糊期权价格.并构造最优化问题,采用二分法算法求解,得到期权模糊价格的最大可信度.我们知道,这一模糊价格无疑是更贴合实际环境.最终投资者可通过判断是否能接受可信度,选择是否能接受这一期权价格,并最终做出投资选择.本文在模型的选择方面,主要考虑了具有浮动敲定价的欧式回望期权的模糊定价模型,并可由此一般推论到具有固定敲定价的欧式回望期权的定价模型和部分回望期权的定价模型.
[Abstract]:With the proposal of "the new normal state of China's economy", the financial market will face a new opportunity and challenge. As a short board in the Chinese financial market, the development of financial derivatives will stabilize the operation of the financial market. Expansion of financial markets is vital, and more relevant to risk management in the real economy. Since early April 1973, when options were first traded on the Chicago options Exchange, We find that the development of the option market is very dynamic. In the option contract, we can clearly know that the option price is the only independent variable that fluctuates with the "supply and demand" of the market. The price of options directly affects the income of both parties in the contract, which leads to the issue of option pricing becoming the core problem in the financial derivatives market. In recent years, in the domestic and foreign financial derivatives trading market, In addition to the European options, American options, which we are most familiar with, ordinary options are also active in a large number of more personalized exotic options derived from standard options. It is a new combination created by derivatives designers to satisfy investors' more individualized investment preferences and cater to market demands. Backdated options are one of the most popular options in the new type. The price of the option becomes more expensive, so how to price the option more accurately is a significant research direction. With the in-depth study of option pricing, it is easy to find out. The financial environment on which the option price depends is very complex and fuzzy. It contains both subjective and objective factors: subjective, influenced by investors' risk preference, and objectively, Affected by non-random uncertainties such as policy and market. Although subjective factors can not be avoided, in order to deal with these resolvable objective non-random uncertainties, we can use the option pricing model. The theory of fuzzy mathematics is introduced. This is also a new direction in the field of finance which has just emerged in recent years. Based on the traditional Black-Scholes option pricing model [2], this paper summarizes the research experience of famous scholars at home and abroad through summing up and sublimating the research experience of famous scholars at home and abroad. It is decided to introduce the fuzzy mathematics theory into the pricing of the lookback option innovatively by means of triangular fuzzy number and expansion principle, and to obtain the fuzzy option price of the lookback option, and to construct the optimization problem, and to solve the problem by using the dichotomy algorithm. Get the maximum credibility of an option's fuzzy price. We know that this fuzzy price is undoubtedly more appropriate to the actual environment. Finally, investors can decide whether they can accept the credibility and choose whether they can accept the option price. In this paper, we mainly consider the fuzzy pricing model of European lookback option with floating knock pricing. The pricing model of European lookback option with fixed knock pricing and the pricing model of partial lookback option can be deduced.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9

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