模糊环境中跳扩散模型下带有交易费用的期权定价方法

发布时间：2018-02-04 06:13

本文关键词： 模糊跳扩散交易费用期权定价　出处：《华中科技大学》2012年硕士论文　论文类型：学位论文

【摘要】：由于金融市场的波动性,许多金融数据不能用确定的数来表示,例如市场无风险利率,波动率等,通常利率为5%左右,波动率为3%左右等等这些具有模糊性的数据,为了描述这些数据模糊数学被引入到金融理论中.一方面,市场中标的资产的价格波动往往有跳跃发生,因此,在期权定价中标的资产的运动模型中应含有跳跃项;另一方面,由于证券交易需要支付交易费用,因此,为了能更好的估计期权价值,交易费用应是一个急需考虑的问题.本文将在Merton跳扩散过程基础上考虑模糊环境中带有交易费用的期权定价问题. 本文主要分为四个部分.第一部分,介绍期权定价理论的产生与发展,包括三方面：跳扩散模型下的期权定价理论研究现状,带有交易费用的期权定价研究现状以及模糊环境下的期权定价研究现状.第二部分,主要利用等价鞅测度方法和概率方法得到跳扩散模型下带有交易费用的欧式看涨期权的定价公式.第三部分,将模糊理论引入到期权定价中.首先,推导出在置信水平a下的期权的价格区间,即投资者在满意度为a的情形下可以选择的期权价格范围;其次,利用优化理论推导出模糊期权价格的隶属度,即给定任意期权价格得到其置信水平a,其经济含义为投资者对期权价格C的满意度为a;最后,为了方便统一定价给出模糊期权的模糊期望.第四部分,在前面所做的工作的基础上,对具体的股票进行数值分析.给出模糊对期权定价的影响,并且得到交易费用对期权价格的影响,也说明了本文研究的合理性.
[Abstract]:Because of the volatility of financial markets, many financial data can not be expressed in certain numbers, such as market risk-free interest rate, volatility, etc., usually interest rate is about 5%. In order to describe the fuzzy data, the volatility is about 3% and so on. In order to describe these data, fuzzy mathematics is introduced into the financial theory. On the one hand, the price volatility of the assets in the market often jumps, so. Jumping items should be included in the motion model of the assets in which the option is priced. On the other hand, in order to better estimate the value of options, because of the transaction costs to be paid for securities trading. Transaction cost should be an urgent problem. This paper will consider the option pricing problem with transaction cost in fuzzy environment on the basis of Merton jump diffusion process. This paper is divided into four parts. The first part introduces the emergence and development of option pricing theory, including three aspects: the current situation of option pricing theory under the jump-diffusion model. The present situation of option pricing with transaction costs and the current situation of option pricing in fuzzy environment. Part two. This paper mainly uses the equivalent martingale measure method and the probability method to get the pricing formula of European call option with transaction cost under jump diffusion model. In the third part, the fuzzy theory is introduced into option pricing. The price range of options under confidence level a is derived, that is, the price range of options that investors can choose when their satisfaction is a. Secondly, the membership degree of the fuzzy option price is deduced by using the optimization theory, that is, given arbitrary option price to obtain its confidence level a, its economic meaning is that the investor's satisfaction with option price C is a; Finally, in order to facilitate the unified pricing of fuzzy options to give the fuzzy expectations. 4th, on the basis of the previous work, the specific stock numerical analysis, and give the impact of fuzzy options pricing. And the influence of transaction cost on option price is obtained, which also shows the rationality of this study.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830;F224

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