基于风险中性概率的几种期权定价模型
发布时间：2019-04-01 17:31
【摘要】：金融数学中的衍生证券定价是人们广泛研究的问题之一,这种证券的定价依赖于与其相关的其它证券的价值.金融期权属于金融衍生证券范畴,期权主要应用于投机和套期保值.套期保值的主要策略是,根据在现货市场买卖情况,交易者可以在期货市场寻求品种、数量相同,但具有相反价格方向的期货合同,用来补偿未来某时刻或者某段时间现货价格变化而带来的风险.为了有效地规避此类风险,准确估计期权的未来价格将是非常重要的,此即期权定价问题. 对于金融产品的定价问题,利用风险中性假设的分析方法是一种常用的方法,风险中性概率的构造是此方法的关键.准确的估计或者近似风险中性概率对于求解此类问题至关重要.在考虑无套利情形下,基于风险中性定价原理,利用三次样条函数作为近似函数替代风险中性概率测度,建立一个期权定价的二次规划模型,效果比较理想.但是此方法只考虑结点处的非负性,没有考虑整体区间上函数非负性,进而建立了结合半正定条件的二次规划模型,保证了近似函数的整体非负性.我们认为二次样条函数依然具有此类性质,并提出了二次样条函数作为近似函数的一个期权定价的二次规划模型,进而也引入了半正定性条件建立了满足整体区间非负性的二次规划模型. 我们将在第一章中介绍问题的背景和发展概况,同时给出本文所需的一些基本概念.对于现有的模型及理论将在第二章给出.在第三章中,重点讨论新构建的两个模型.第四章,一系列数值实验说明了新模型的有效性；结论部分简要地介绍了本文所取得的主要成果.
[Abstract]:The pricing of derivative securities in financial mathematics is one of the widely studied problems. The pricing of these securities depends on the value of other securities related to them. Financial options belong to the category of financial derivative securities, which are mainly used in speculation and hedging. The main strategy of hedging is that, depending on the situation of buying and selling in the spot market, traders can seek varieties in the futures market in the same number, but have futures contracts with opposite price directions. Used to compensate for future changes in spot prices at some point or time. In order to avoid this kind of risk effectively, it is very important to accurately estimate the future price of options, which is called option pricing problem. For the pricing problem of financial products, the analysis method of risk neutral hypothesis is a common method, and the construction of risk neutral probability is the key of this method. Accurate estimation or approximate risk neutral probability is very important for solving this kind of problem. In the case of no arbitrage, based on the principle of risk neutral pricing, the cubic spline function is used as an approximate function to replace the risk neutral probability measure, and a quadratic programming model of option pricing is established. The result is satisfactory. However, this method only considers the nonnegativity of the nodes and does not consider the nonnegativity of the functions on the whole interval. Furthermore, a quadratic programming model combined with the semi-positive definite conditions is established, which ensures the global nonnegativity of the approximate function. We consider that quadratic spline function still has this kind of property, and propose a quadratic programming model for option pricing of quadratic spline function as an approximate function. Then the semi-positive definite condition is introduced to establish the quadratic programming model which satisfies the global interval nonnegativity. In the first chapter, we will introduce the background and development of the problem, and give some basic concepts needed in this paper. The existing models and theories will be given in the second chapter. In the third chapter, we focus on the two newly constructed models. In chapter 4, a series of numerical experiments show the validity of the new model, and the main results obtained in this paper are briefly introduced in the conclusion.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
本文编号：2451739
[Abstract]:The pricing of derivative securities in financial mathematics is one of the widely studied problems. The pricing of these securities depends on the value of other securities related to them. Financial options belong to the category of financial derivative securities, which are mainly used in speculation and hedging. The main strategy of hedging is that, depending on the situation of buying and selling in the spot market, traders can seek varieties in the futures market in the same number, but have futures contracts with opposite price directions. Used to compensate for future changes in spot prices at some point or time. In order to avoid this kind of risk effectively, it is very important to accurately estimate the future price of options, which is called option pricing problem. For the pricing problem of financial products, the analysis method of risk neutral hypothesis is a common method, and the construction of risk neutral probability is the key of this method. Accurate estimation or approximate risk neutral probability is very important for solving this kind of problem. In the case of no arbitrage, based on the principle of risk neutral pricing, the cubic spline function is used as an approximate function to replace the risk neutral probability measure, and a quadratic programming model of option pricing is established. The result is satisfactory. However, this method only considers the nonnegativity of the nodes and does not consider the nonnegativity of the functions on the whole interval. Furthermore, a quadratic programming model combined with the semi-positive definite conditions is established, which ensures the global nonnegativity of the approximate function. We consider that quadratic spline function still has this kind of property, and propose a quadratic programming model for option pricing of quadratic spline function as an approximate function. Then the semi-positive definite condition is introduced to establish the quadratic programming model which satisfies the global interval nonnegativity. In the first chapter, we will introduce the background and development of the problem, and give some basic concepts needed in this paper. The existing models and theories will be given in the second chapter. In the third chapter, we focus on the two newly constructed models. In chapter 4, a series of numerical experiments show the validity of the new model, and the main results obtained in this paper are briefly introduced in the conclusion.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
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相关硕士学位论文 前2条
1 胡之英;几种模型下欧式期权定价的研究[D];陕西师范大学;2008年
2 梁淑平;欧式期权和美式期权定价的数值方法进一步研究[D];中南大学;2008年
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