本文選題：奇異期權(quán) + 幾何布朗運動�。� 參考：《湘潭大學》2013年碩士論文

【摘要】：期權(quán)交易起始于十八世紀后期的美國和歐洲市場,在其后的幾十年里,期權(quán)定價理論以及應用方面的研究迅速發(fā)展,并且取得了豐碩的成果。B-S期權(quán)定價公式是在經(jīng)典的資本市場理論下建立的模型。由于這種研究忽略了金融市場的非線性分形以及其復雜性,經(jīng)典的資本主義市場具有局限性,到現(xiàn)在已經(jīng)不適應深層次的金融市場需要。因此需要我們研究定位在更廣泛的環(huán)境中,使其具有更加實用的價值。 在有效市場假說下,標的資產(chǎn)的價格過程都是幾何布朗運動。可是,標的資產(chǎn)的波動一般具有自相似性和長期依賴等特征,我們知道幾何布朗運動沒有相應的性質(zhì),這就會導致幾何布朗運動與市場存在著一定程度上的差距,因此并不是刻畫標的資產(chǎn)價格的最理想的工具。而分數(shù)布朗運動是具有長期依賴性的自相似過程,因此,用分數(shù)布朗運動代替幾何布朗運動可以很好地描述標的資產(chǎn)的價格過程,并能更貼切實際市場的結(jié)果,從而就有更好的適應性。研究者也發(fā)現(xiàn),當實際市場出現(xiàn)一些重大的信息時,價格的變化過程并不是連續(xù)的,我們采用跳-擴散模型來反映這一不連續(xù)的特性。 本文是建立在分數(shù)跳-擴散模型下的奇異期權(quán)的定價研究,主要成果如下： 第一、基于分數(shù)跳-擴散模型下的上限型買權(quán)的定價。 第二、基于分數(shù)跳-擴散模型下的抵付型買權(quán)的定價。 第三、基于分數(shù)跳-擴散模型下的局部支付型買權(quán)的定價。 第四、基于分數(shù)跳-擴散模型下的二項式變異期權(quán)的定價。
[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.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F830.9;F224;O211.6

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相關(guān)期刊論文 前2條

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2 林怡;;標的資產(chǎn)服從分數(shù)跳-擴散過程的上限型買權(quán)的期權(quán)定價[J];商場現(xiàn)代化;2010年29期

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本文編號：1868853