基于Python科学计算包的金融应用实现

发布时间：2018-05-25 07:25

本文选题：金融应用 + IPython　；参考：《江西财经大学》2017年硕士论文

【摘要】：金融已经渗透到生活的各个领域,因此需要对金融的趋势加以研判,这样就诞生了金融建模。金融建模是运用数学工具来定量研究金融问题的一门学科。在完成金融建模后需要使用计算机进行求解和模拟仿真。常见的金融模型包括:最优求解、期权模型、资本资产定价模型和资产组合理论。而计算机求解和模拟仿真软件包括 C++、Excel VBA、Matlab、Python 等。C++语言由于抽象程度不高,不是面向领域的,其导致学习难度高。Excel VBA则可扩展性差,无法应用求解实际问题。Matlab虽然是面向领域的,但其不是通用语言,无法与Web等很好整合。本文采用免费的Python语言为计算机求解和模拟仿真语言。具体来说,就是使用Python科学计算的集成开发环境Anaconda3中的IPython Notebook。IPython Notebook将程序代码、问题描述、数学公式和图形完美结合,这使得其易于学习。由于现有中文Python科学计算包资料不够完整,本文给出Python科学计算包中的Numpy、Scipy、Sympy和matplotlib相关功能调用说明。在此基础上,讨论效用最优和期权模型中的蒙特卡罗仿真方法。具体来说,首先介绍多维数组Numpy包的数据定义功能,然后给出其在投入产出方面的应用实例。其次,给出符号计算包Sympy的功能,然后给出其通过海森矩阵在多元极值方面的应用。第三,在介绍科学计算包Scipy的基础上,给出了拉格朗日乘数法求解受限极值问题。最后,给出了绘图包matplotlib的常见功能,给出了蒙特卡罗方法在期权估值方面的应用。本文所有例子均给出了调试通过的完整ipynb源程序。
[Abstract]:Finance has infiltrated into every field of life, so we need to judge the trend of finance, so financial modeling is born. Financial modeling is a discipline that uses mathematical tools to quantitatively study financial problems. After the financial modeling is completed, it is necessary to use computer to solve and simulate. Common financial models include: optimal solution, option model, capital asset pricing model and portfolio theory. However, the computer solution and simulation software, such as C # Excel VBA / Matlab / Python and so on, is not domain oriented because of its low degree of abstraction, which leads to the difficulty of learning. Excel VBA is not extensible. Although Matlab is domain oriented, it is not a general language and can not be well integrated with Web and so on. In this paper, the free Python language is used as the computer solution and simulation language. Specifically, using IPython Notebook.IPython Notebook in Anaconda3, an integrated development environment for Python scientific computing, combines program code, problem description, mathematical formulas and graphics perfectly, which makes it easy to learn. Due to the incomplete data of the existing Chinese Python scientific computing package, this paper gives the description of the related functions of Numpy Scipyy Sympy and matplotlib in the Python Science Computing package. On this basis, the Monte Carlo simulation method in the utility optimal and option models is discussed. Specifically, the data definition function of multidimensional array Numpy package is introduced firstly, and then its application in input-output is given. Secondly, the function of symbolic computing packet Sympy is given, and then its application to multivariate extremum through Heyson matrix is given. Thirdly, on the basis of introducing the scientific computing package Scipy, the Lagrange multiplier method is given to solve the constrained extremum problem. Finally, the common functions of drawing package matplotlib are given, and the application of Monte Carlo method in option estimation is given. In this paper, all examples are given through the debugging of the complete ipynb source program.
【学位授予单位】：江西财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F830;TP312

【参考文献】