带跳过程驱动的金融市场中期权定价问题研究

发布时间：2018-04-29 03:07

本文选题：期权 + Levy过程　；参考：《北京邮电大学》2013年硕士论文

【摘要】：几年来,随着金融市场的蓬勃发展,期权定价理论成为数理金融的一个研究重点。由于期权具有良好的规避风险,风险投资和价值发现等功能,且表现出灵活性和多样性的特点,期权理论成为现代金融学的重要组成部分,对其定价理论的研究对于学术界,交易所和柜台交易市场乃至整个金融业都具有非常重要的意义。这个课题主要研究了跳跃过程驱动的金融市场上未定权益期权的定价,主要从两个方面进行尝试： (一)在研究未定权益定价的过程中,为了适应复杂的金融市场环境,研究者已将标的资产价格过程从一般的几何布朗运动扩充到跳跃扩散模型中的泊松过程,再到更加复杂的跳跃过程-Levy过程,同时呢,研究者发现过去重大事件会对标的资产的当前价格产生影响,也就是说带一定的时间延迟效用,所以本课题结合Corcuera,J.M.和Nualart,D.等学者在Levy过程驱动模型下的研究成果,第一部分主要是研究了标的资产价格在Levy过程驱动下带时间延迟的金融模型中的未定权益的定价。 (二)对于一种新型的奇异期权——亚式期权来说,它的形式有很多,基于不同的形式,学者们研究的内容也不同,本课题基于跳跃扩散模型,第二部分主要研究了标的资产价格服从跳跃扩散模型时,连续几何平均亚式期权的定价公式和平价公式。
[Abstract]:In recent years, with the rapid development of financial market, option pricing theory has become a research focus of mathematical finance. Option theory has become an important part of modern finance because of its good functions of avoiding risk, venture capital and value discovery, and showing the characteristics of flexibility and diversity. Exchanges and over-the-counter trading markets and even the financial industry as a whole have very important significance. This topic mainly studies the pricing of undetermined equity options in the financial market driven by the jump process, mainly from two aspects: (1) in order to adapt to the complex financial market environment, researchers have extended the underlying asset price process from the general geometric Brownian motion to the Poisson process in the jump diffusion model. At the same time, the researchers found that major events in the past have an impact on the current price of the underlying asset, that is, with a certain time-delay utility, so this topic combines with Corcueraj J. M. And Nualartd D. The first part is to study the pricing of uncertain equity in the financial model with time delay of underlying asset price driven by Levy process. (2) for a new type of strange option--Asian option, there are many forms, based on different forms, scholars also study different content, this topic is based on jump diffusion model. In the second part, the pricing formula and parity formula of continuous geometric average Asian option are studied.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;O211.6

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