有时滞影响的择好期权定价研究

发布时间：2018-05-06 18:22

本文选题：等价鞅测度 + 股票　；参考：《湖南大学》2012年硕士论文

【摘要】：期权定价的Black-Scholes模型中,假设股票价格波动率为常数.然而大量的实证研究发现股票的收益波动率并非常数且与过去的股票价格有关(即具有时滞因素的影响).本文在Arriojas和李亚琼等对于具有时滞的单风险资产期权研究的基础上,扩展研究了两个风险资产均具有时滞影响的欧式择好期权定价问题.本文所做的主要工作如下： (1)基于李亚琼,黄立宏的研究结果,在股票支付连续红利情形下,讨论了时滞对欧式期权价格的影响,并得到一些结论. (2)在Arriojas等具有时滞的研究框架下,采用计价单位变换、等价鞅测度理论、风险中性和无套利原理的概率论方法研究了具时滞影响的欧式择好期权定价,在持有期的一个子区间上得到了不支付红利和支付连续红利两种情形下的期权价格的闭式解,同时又采用偏微分方程的方法对其定价公式进行验证. (3)对(2)中在两种能得到闭式解的情形下进行比较静态分析,进一步了解主要参数对期权价格的影响,及其结论与不具有时滞的情况之间的差异. 研究发现：(1)无论股票是否支付红利,在最简单的随机波动率假设下,时滞对欧式期价格的影响与当前时刻和到期时刻的滞后股票价格有关.(2)具有时滞的择好期权价格不仅与当前时刻的股票价格有关,还与股票过去的价格有关.(3)无论股票是否支付红利,具有时滞的择好期权价格随股票当前价格的增加而增加,且是股票当前价格的凸函数.而择好期权价格受存续期的影响与股票是否支付红利有关.另外,时滞因素只会影响择好期权的价格与股票价格、存续期之间关系存在的区间大小,并不会改变择好期权的价格与股票价格、存续期之间的本质关系.
[Abstract]:On the basis of the research on single - risk asset options with time - lag , the author expands the research on the pricing of European options with time - lag effects on two risk assets based on the research on single - risk asset options with time lag . The main work is as follows :

( 1 ) Based on the research results of Li Yanqiong and Huang Lihong , the influence of time lag on European option price is discussed in the case of continuous dividend payment , and some conclusions are obtained .

( 2 ) Under the research framework with time lag , such as Arrio. et al . , the pricing unit transform , the equivalent Martingales measure theory , the risk neutral and the non - arbitrage principle are adopted to study the European option pricing with time lag , and the closed solution of the option price is obtained in one sub - section of the same period without paying dividends and paying continuous dividend . At the same time , the pricing formula is verified by the method of partial differential equation .

( 3 ) The comparative static analysis is carried out in the case of two kinds of closed solutions in ( 2 ) , further understanding the influence of the main parameters on the options price , and the difference between the conclusion and the case without delay .

It is found that ( 1 ) No matter whether the stock pays dividends , under the assumption of the simplest random fluctuation rate , the influence of time lag on the European period price is related to the current time and the lag stock price at the current time and due time . ( 2 ) The option price with time lag is not only related to the stock price at the current time , but also the convex function of the current price of the stock .

【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

【参考文献】