不确定环境下的脆弱期权定价研究

发布时间：2018-01-01 04:18

本文关键词：不确定环境下的脆弱期权定价研究　出处：《华南理工大学》2013年硕士论文　论文类型：学位论文

【摘要】：期权作为一种金融衍生产品，在金融市场上扮演着十分重要的角色。因而，对其进行准确有效的定价就显得异常重要。Black和Scholes于20世纪70年代提出了著名的B-S期权定价模型。该模型对交易员如何定价和对冲期权产生了深远的影响，并对金融工程领域的发展起到了巨大的促用。然而，随着金融市场的快速发展，这一模型所固有的缺陷开始显露出来，并制约了期权市场的进一步发展。其中表现比较明显的是期权交易过程中的信用风险。所以，如何调整期权的价格来反映交易对手的信用风险就成为一个亟待解决的问题。这一问题也就是通常所说的脆弱期权定价问题。本文在定价脆弱期权的结构模型的基础上，主要从以下三个方面对美式脆弱期权和欧式脆弱期权的定价进行了研究。首先， Klein（2010）基于Hull和White（1995）提出的三维二叉树方法的思想，将其运用到美式脆弱期权定价研究中，为了得到更加准确有效的美式脆弱期权价格，本文引入三叉树代替二叉树对标的股票价格及交易对手资产价值进行刻画，在此基础上构建了定价美式脆弱期权的三维三叉树模型。根据这一模型，我们给出了一些数值例子，这些数值例子很好地分析了美式脆弱期权的性质。其次，本文在考虑运用几何Lévy过程描述标的股票价格波动的基础上，依据Klein（1996）提出的定价欧式脆弱期权的模型框架，构建了一个基于Lévy过程的定价欧式脆弱期权的修正模型。考虑到金融市场的时常波动性和市场投资者所面临的信息的非完全准确性所导致的市场参数的不确定性，本文在修正的脆弱期权定价模型的基础上，进一步引入模糊集理论，通过假定无风险利率、波动率、平均跳跃强度以及资产收益率为三角模糊数，得到了模糊环境下基于Lévy过程的欧式脆弱期权定价模型。同时，本文通过一些数值例子对修正模型和Klein（1996）模型进行了比较分析。最后，Xu（2012）在假定股票价格和交易对手的资产价值均服从跳跃扩散过程的情况下，给出了定价脆弱期权的模型。考虑到影响金融市场的因素较多所导致的市场参数的不确定性，本文在Xu（2012）的基础上，引入模糊集理论，通过假定无风险利率，波动率以及其平均跳跃强度为三角模糊数，，运用Wu（2004）提供的模糊数运算法则，得到了定价欧式脆弱期权的模糊跳跃扩散模型，并最终给出了模型的相应算法步骤。运用该模型算法，投资者不仅可以根据自己满意的隶属度选择相应的期权进行投资，而且还可以计算给定期权价格所对应的隶属度。同时，本文针对新模型给出了一些数值例子，并通过这些数值例子对模糊模型、Xu（2012）模型以及Klein（1996）模型进行了比较分析。数例结果表明，本文提出的定价脆弱期权的方法，能够更加准确有效地对脆弱期权进行定价，从而可以引导金融投资者们更加有效地进行决策。
[Abstract]:As a financial derivative, option plays a very important role in the financial market. Black and Scholes put forward the famous B-S option pricing model in 1970s. Punching options have had a profound impact. It has greatly promoted the development of financial engineering. However, with the rapid development of financial markets, the inherent defects of this model began to show. It also restricts the further development of the option market. Among them, the more obvious performance is the credit risk in the process of option trading. How to adjust the price of options to reflect the credit risk of counterparty is an urgent problem to be solved. On... The pricing of American fragile options and European fragile options is studied from the following three aspects. First of all, Klein 2010) is based on the idea of three-dimensional binary tree proposed by Hull and White 1995, and applies it to the study of American fragile option pricing. In order to get more accurate and effective American fragile option price, this paper introduces tri-tree instead of binary tree to describe the underlying stock price and counterparty asset value. On the basis of this, we construct a three dimensional triple tree model for pricing American fragile options. According to this model, we give some numerical examples, which give a good analysis of the properties of American fragile options. Secondly, on the basis of considering the geometric L 茅 vy process to describe the volatility of the underlying stock price, this paper proposes a model framework for pricing European fragile options according to Klein's 1996. A modified model of pricing European fragile options based on L 茅 vy process is constructed. Considering the frequent volatility of financial markets and the incomplete accuracy of information faced by market investors, the market parameters are not satisfied. Certainty. On the basis of the modified fragile option pricing model, this paper further introduces the fuzzy set theory, which assumes that the risk-free interest rate, volatility, average jump intensity and return rate of assets are triangular fuzzy numbers. A European vulnerable option pricing model based on L 茅 vy process in fuzzy environment is obtained. At the same time, the modified model and Kleinnberg 1996) model are compared and analyzed by some numerical examples. Finally, Xue Xue (2012) assumes that both the stock price and the asset value of the counterparty are subject to the jump diffusion process. The model of pricing vulnerable options is given. Considering the uncertainty of market parameters caused by many factors affecting financial market, fuzzy set theory is introduced on the basis of Xuan2012). Based on the assumption that the risk-free interest rate, volatility and its average jump intensity are triangular fuzzy numbers, the fuzzy number algorithm provided by Wuwei 2004 is used. The fuzzy jump diffusion model for pricing European fragile options is obtained, and the corresponding algorithm steps are given. Investors can not only select the corresponding options according to their own satisfactory membership degree, but also calculate the corresponding membership degree of a given option price. At the same time, this paper gives some numerical examples for the new model. These numerical examples are used to compare and analyze the fuzzy model Xujia2012) and the Kleinfen 1996) model. The results of several examples show that the method proposed in this paper can price fragile options more accurately and effectively, thus leading financial investors to make more effective decisions.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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