随机利率下的两值期权定价

发布时间：2018-02-12 10:42

本文关键词： 两值期权随机利率计价单位转换 Girsanov定理附息债券　出处：《南京师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：近几年,金融衍生品市场发展迅猛,尤其是期权的发展,对风险规避,风险投资和价值发现等金融领域产生了深远的影响。相应的,期权定价也成为了金融数学最重要的部分之一。目前,金融市场中产生了大量的新型衍生产品,两值期权就是其中典型的一种,人们对利率是常数的情形下的两值期权的定价问题作了许多研究并得到了一些结果,但金融市场上,受多种因素影响,利率往往是一个随机的变量。在本篇论文中,主要通过无套利理论及转换计价单位的方法,对随机利率下两值期权的定价问题进行了研究,主要的结果如下： (1)当标的资产是股票时,本文分别讨论了一维和多维情形下,两值期权的定价问题,给出了定价公式,同时,讨论了随机利率情形下,两值期权与欧式看涨期权之间的关系,并通过该关系给出了随机利率情形下,欧式看涨期权的定价公式。 (2)当标的资产是零息债券时,本文给出了两值期权的定价公式；当标的资产是附息债券时,本文同样给出了其定价方法。
[Abstract]:In recent years, the financial derivatives market has developed rapidly, especially the development of options, which has had a profound impact on the financial fields such as risk aversion, venture capital and value discovery. Option pricing has also become one of the most important parts of financial mathematics. At present, a large number of new derivatives have been produced in the financial market. Two-valued option is one of the typical ones. People have done a lot of research and got some results on the pricing of two-valued options when the interest rate is constant. But in financial markets, interest rates are often a random variable affected by many factors. In this paper, the pricing problem of two-valued options under stochastic interest rate is studied by means of the no-arbitrage theory and the method of converting pricing units. The main results are as follows:. 1) when the underlying asset is a stock, this paper discusses the pricing problem of two-valued options under one-dimensional and multi-dimensional cases, and gives the pricing formula. At the same time, the relationship between two-valued options and European call options is discussed in the case of stochastic interest rate. Through this relation, the pricing formula of European call option is given. 2) when the underlying asset is a zero interest bond, this paper gives the pricing formula of the two-valued option, and when the underlying asset is an interest-bearing bond, the pricing method is also given in this paper.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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