英文标题：
《Common Decomposition of Correlated Brownian Motions and its Financial
Applications》
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作者：
Tianyao Chen, Xue Cheng, Jingping Yang
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最新提交年份：
2020
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英文摘要：
In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, $(X,Y,T)$, where $X$ and $Y$ are independent Brownian motions. We show the equivalent conditions for the triplet being independent. We discuss the connection and difference of the common decomposition with the local correlation model. Indicated by the discussion, we propose a new method for constructing correlated Brownian motions which performs very well in simulation. For applications, we use these very general results for pricing two-factor financial derivatives whose payoffs rely very much on the correlations of underlyings. And in addition, with the help of numerical method, we also make a discussion of the pricing deviation when substituting a constant correlation model for a general one.
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中文摘要：
本文发展了两个相关布朗运动的公共分解理论，其中，利用时间变换方法，相关布朗运动用三重过程$（X，Y，T）$表示，其中$X$和$Y$是独立的布朗运动。我们给出了三重态独立的等价条件。讨论了公共分解与局部相关模型的联系和区别。讨论表明，我们提出了一种构造相关布朗运动的新方法，该方法在模拟中表现良好。在应用中，我们使用这些非常普遍的结果为双因素金融衍生品定价，其收益在很大程度上依赖于基础的相关性。此外，借助数值方法，我们还讨论了用常相关模型代替一般模型时的定价偏差。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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