偏微分方程在两类期权定价问题中的应用

发布时间：2018-11-09 08:59

【摘要】：随着期权市场的不断发展,对于各种期权的定价研究也越来越多.虽然传统的B-S公式给出了一股的期权定价公式,但是,为了更加贴近现实,本文尝试在B-S的基础上对永久美式经理人股票期权给出存在障碍情形下的定价模型,并且对含有预设兑换率的外汇期权在本国和外国短期利率各自满足Vasiceek模型的情形下,对期权进行定价研究. 经理人股票期权作为一种激励性的薪酬工具,被越来越多的国家广泛应用,并且自2005年开始,美国财务会计准则委员会要求公司把经理人股票期权的价值公示出来,由此对期权的估值变得更加重要.此外,由于国际金融贸易一体化的趋势日益明显,外汇风险的规避问题也成为学者研究的课题之一,所以研究利率对外汇期权的影响是十分有意义的.文中研究了一种新的外汇期权,投资者可以利用这种含预设兑换率的外汇期权来规避一部分风险. 本文首先在第一章中介绍了经理人股票期权的发展和现状以及本文所要解决的问题.在第二章中给出了在存在等待期和卖出限制的情形下,永久美式经理人股票期权的定价模型以及不同参数对经理人股票期权价值的影响.第三章在随机利率模型下,分别给出了含有预设兑换率的外汇看涨期权和看跌期权的定价公式.
[Abstract]:With the development of option market, there are more and more researches on option pricing. Although the traditional B-S formula gives a stock option pricing formula, in order to get closer to the reality, this paper attempts to give the pricing model of the permanent American executive stock option on the basis of B-S. Furthermore, the pricing of foreign currency options with preset exchange rate is studied under the condition that the short-term interest rates of both countries satisfy the Vasiceek model. As an incentive compensation tool, ESO has been widely used in more and more countries. Since 2005, the Financial Accounting Standards Board (FASB) has asked companies to disclose the value of ESO. As a result, the valuation of options becomes even more important. In addition, as the trend of international financial and trade integration is becoming more and more obvious, the problem of foreign exchange risk avoidance has become one of the topics studied by scholars, so it is very meaningful to study the influence of interest rate on foreign exchange options. In this paper, a new foreign exchange option is studied, which can be used by investors to avoid some risks. In the first chapter, this paper introduces the development and current situation of executive stock option and the problems to be solved in this paper. In the second chapter, the pricing model of permanent American executive stock option and the influence of different parameters on the value of executive stock option are given under the condition of waiting period and selling limit. In chapter 3, under the stochastic interest rate model, the pricing formulas of foreign exchange call options and put options with preset exchange rate are given respectively.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O175.2;F830.9

【共引文献】