分数跳—扩散模型的奇异期权定价

发布时间：2018-05-10 09:58

本文选题：奇异期权 + 几何布朗运动　；参考：《湘潭大学》2013年硕士论文

【摘要】：期权交易起始于十八世纪后期的美国和欧洲市场,在其后的几十年里,期权定价理论以及应用方面的研究迅速发展,并且取得了丰硕的成果。B-S期权定价公式是在经典的资本市场理论下建立的模型。由于这种研究忽略了金融市场的非线性分形以及其复杂性,经典的资本主义市场具有局限性,到现在已经不适应深层次的金融市场需要。因此需要我们研究定位在更广泛的环境中,使其具有更加实用的价值。在有效市场假说下,标的资产的价格过程都是几何布朗运动。可是,标的资产的波动一般具有自相似性和长期依赖等特征,我们知道几何布朗运动没有相应的性质,这就会导致几何布朗运动与市场存在着一定程度上的差距,因此并不是刻画标的资产价格的最理想的工具。而分数布朗运动是具有长期依赖性的自相似过程,因此,用分数布朗运动代替几何布朗运动可以很好地描述标的资产的价格过程,并能更贴切实际市场的结果,从而就有更好的适应性。研究者也发现,当实际市场出现一些重大的信息时,价格的变化过程并不是连续的,我们采用跳-扩散模型来反映这一不连续的特性。本文是建立在分数跳-扩散模型下的奇异期权的定价研究,主要成果如下：第一、基于分数跳-扩散模型下的上限型买权的定价。第二、基于分数跳-扩散模型下的抵付型买权的定价。第三、基于分数跳-扩散模型下的局部支付型买权的定价。第四、基于分数跳-扩散模型下的二项式变异期权的定价。
[Abstract]:Option trading began in the American and European markets in the late 18th century. In the following decades, the research on option pricing theory and its application developed rapidly. And has obtained the rich achievement. The B-S option pricing formula is established under the classical capital market theory model. Because this kind of research neglects the nonlinear fractal and its complexity of the financial market, the classical capitalist market has its limitations, so it has been unable to meet the needs of the deep financial market. Therefore, we need to study positioning in a broader environment to make it more practical value. Under the efficient market hypothesis, the price process of underlying assets is geometric Brownian motion. However, the fluctuation of underlying assets generally has the characteristics of self-similarity and long-term dependence. We know that geometric Brownian motion has no corresponding properties, which will lead to a certain extent gap between geometric Brownian motion and market. Therefore, it is not the best tool to describe the underlying asset price. The fractional Brownian motion is a self-similar process with long-term dependence. Therefore, using fractional Brownian motion instead of geometric Brownian motion can well describe the price process of the underlying asset and be more appropriate to the results of the actual market. So there is better adaptability. The researchers also find that the process of price change is not continuous when there are some important information in the actual market. We use the jump-diffusion model to reflect this discontinuity. This paper is a study on the pricing of singular options based on fractional hop-diffusion model. The main results are as follows: First, the pricing of upper-limit buying rights based on fractional jump-diffusion model. Secondly, based on the fractional hopping-diffusion model, the pricing of the countervailing right is discussed. Thirdly, the pricing of local payment right based on fractional hopping diffusion model. Fourth, the pricing of binomial variant options based on fractional hopping-diffusion model.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224;O211.6

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