广义指数O-U过程下的欧式复杂任选期权定价
发布时间：2018-11-18 17:56
【摘要】：期权作为一种金融衍生工具,在金融市场中扮演着十分重要的角色,对其进行有效的定价也显得尤为重要.近几年,由于金融市场发展迅速,出现了许多新型期权,这些期权在许多方面与标准期权发生变异,被称为奇异期权.任选期权就是奇异期权的一种,它允许期权持有者在早于期权到期日的某一时间决定此期权是看涨期权还是看跌期权,此时间之后即为标准欧式期权.任选期权能有效防范风险,降低持有者的投资成本.因此,如何对任选期权进行合理有效的定价已成为现在研究的热点话题.本文主要是对复杂任选期权进行定价.首先假设股票价格服从连续广义指数O-U过程模型,无风险利率以及股票价格的期望回报率、波动率均为时间的函数,用鞅方法和保险精算方法分别给出了复杂任选期权在任意时刻t的价格的解析解.然而,在实际金融市场中股票价格会突然出现跳跃,连续过程无法准确刻画股票价格的波动.因此,本文又假设股票价格服从跳扩散广义指数O-U过程模型,更加准确的刻画了股票价格波动的实际情况,并再次用鞅方法和保险精算方法分别给出了复杂任选期权在任意时刻t的价格的解析解.
[Abstract]:As a kind of financial derivative, option plays a very important role in financial market. In recent years, due to the rapid development of the financial market, there are many new options, these options and standard options in many ways have changed, known as strange options. An optional option is one of the exotic options, which allows the holder of an option to decide whether the option is a call option or a put option at a time earlier than the expiration date of the option, after which time it is a standard European option. Optional options can effectively guard against risk and reduce the investment cost of the holder. Therefore, how to make reasonable and effective pricing of optional options has become a hot topic. This article mainly carries on the pricing to the complex optional option. First of all, assume that the stock price service from the continuous generalized index O-U process model, risk-free interest rate and the expected rate of return of stock prices, volatility is a function of time, By means of martingale method and actuarial method, the analytical solutions of the price of complex optional options at any time t are given respectively. However, in the actual financial market, the stock price will suddenly jump, continuous process can not accurately describe the volatility of stock prices. Therefore, this paper assumes the generalized index O-U process model of stock price from jump diffusion to describe the actual situation of stock price fluctuation more accurately. Then the analytical solution of the price of complex optional options at any time t is given by using martingale method and actuarial method respectively.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9
本文编号：2340726
[Abstract]:As a kind of financial derivative, option plays a very important role in financial market. In recent years, due to the rapid development of the financial market, there are many new options, these options and standard options in many ways have changed, known as strange options. An optional option is one of the exotic options, which allows the holder of an option to decide whether the option is a call option or a put option at a time earlier than the expiration date of the option, after which time it is a standard European option. Optional options can effectively guard against risk and reduce the investment cost of the holder. Therefore, how to make reasonable and effective pricing of optional options has become a hot topic. This article mainly carries on the pricing to the complex optional option. First of all, assume that the stock price service from the continuous generalized index O-U process model, risk-free interest rate and the expected rate of return of stock prices, volatility is a function of time, By means of martingale method and actuarial method, the analytical solutions of the price of complex optional options at any time t are given respectively. However, in the actual financial market, the stock price will suddenly jump, continuous process can not accurately describe the volatility of stock prices. Therefore, this paper assumes the generalized index O-U process model of stock price from jump diffusion to describe the actual situation of stock price fluctuation more accurately. Then the analytical solution of the price of complex optional options at any time t is given by using martingale method and actuarial method respectively.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9
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