英文标题：
《A High Order Method for Pricing of Financial Derivatives using Radial
  Basis Function generated Finite Differences》
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作者：
Slobodan Milovanovi\\\'c and Lina von Sydow
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最新提交年份：
2018
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英文摘要：
  In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher accuracy. Still, the discretization matrix is fairly sparse. As a model problem, we consider the pricing of European options in 2D. Since such options have a discontinuity in the first derivative of the payoff function which prohibits high order convergence, we smooth this function using an established technique for Cartesian grids. Numerical experiments show that we acquire a fourth order scheme in space, both for the uniform and the nonuniform node layouts that we use. The high order method with the nonuniform node layout achieves very high accuracy with relatively few nodes. This renders the potential for solving pricing problems in higher spatial dimensions since the computational memory and time demand become much smaller with this method compared to standard techniques.
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中文摘要：
在本文中，我们考虑使用径向基函数生成的空间有限差分对金融衍生品进行数值定价。这种离散化方法的优点是不需要笛卡尔网格。相反，可以在需要更高精度的区域以更高的密度放置节点。尽管如此，离散化矩阵还是相当稀疏的。作为一个模型问题，我们考虑了二维欧式期权的定价问题。由于这类期权在支付函数的一阶导数中具有不连续性，从而禁止高阶收敛，因此我们使用笛卡尔网格的既定技术对该函数进行平滑处理。数值实验表明，对于我们使用的均匀和非均匀节点布局，我们在空间中获得了一个四阶格式。采用非均匀节点布局的高阶方法可以在节点相对较少的情况下获得非常高的精度。与标准技术相比，这种方法的计算内存和时间需求变得更小，因此有可能在更高的空间维度上解决定价问题。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Computer Science        计算机科学
二级分类：Computational Engineering, Finance, and Science        计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Numerical Analysis        数值分析
分类描述：cs.NA is an alias for math.NA. Roughly includes material in ACM Subject Class G.1.
cs.na是Math.na的别名。大致包括ACM学科类G.1的材料。
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一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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