一类算术平均亚式期权定价的算法研究

发布时间：2018-08-13 12:45

【摘要】：亚式期权是一种强路径依赖型期权,已成为金融市场中最活跃的新型期权之一,其定价问题也已成为金融衍生资产定价研究的热点问题。本文研究了一类新型的算术平均亚式期权—储蓄亚式期权定价问题。储蓄亚式期权既保留了美亚期权定价可提前执行的灵活性,又比经典的亚式期权具有更多优点。在风险中性的假设下,我们对一致二叉树股票价格模型中的储蓄亚式期权定价进行了深入研究,给出了为这类期权定价进行近似计算的数值方法。该方法采用随机抽取代表状态计算储蓄亚式期权期望收益的近似值,同时给出了误差估计及其置信度。这在理论上更为完善,也更贴近现实,克服了亚式期权定价近似计算的AM0算法对状态选取的局限性。
[Abstract]:Asian option is a strong path dependent option and has become one of the most active new options in the financial market. The pricing of Asian option has also become a hot issue in the research of financial derivative asset pricing. In this paper, we study a new type of arithmetic average Asian option-savings Asian option pricing problem. Savings Asian option not only retains the flexibility of American Asian option pricing, but also has more advantages than the classical Asian option. Under the assumption of risk neutrality, we deeply study the pricing of savings Asian options in the uniform binary tree stock price model, and give a numerical method to approximate the pricing of this kind of options. In this method, the approximate value of the expected income of the savings Asian option is calculated by using the random sampling representative state, and the error estimate and its confidence are given at the same time. This method is more perfect in theory and closer to reality. It overcomes the limitation of AM0 algorithm of Asian option pricing approximation to state selection.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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