英文标题：
《Numerical pricing of American options under two stochastic factor models
with jumps using a meshless local Petrov-Galerkin method》
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作者：
Jamal Amani Rad and Kourosh Parand
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最新提交年份：
2014
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英文摘要：
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that these methods depend strongly on the mesh properties which is the major disadvantage of them. Therefore, we propose the use of the meshless methods to solve the aforementioned options models, especially in this work we select and analyze one scheme of them, named local radial point interpolation (LRPI) based on Wendland\'s compactly supported radial basis functions (WCS-RBFs) with C6, C4 and C2 smoothness degrees. The LRPI method which is a special type of meshless local Petrov-Galerkin method (MLPG), offers several advantages over the mesh-based methods, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. These schemes are the truly meshless methods, because, a traditional non-overlapping continuous mesh is not required, neither for the construction of the shape functions, nor for the integration of the local sub-domains. In this work, the American option which is a free boundary problem, is reduced to a problem with fixed boundary using a Richardson extrapolation technique. Then the implicit-explicit (IMEX) time stepping scheme is employed for the time derivative which allows us to smooth the discontinuities of the options\' payoffs. Stability analysis of the method is analyzed and performed. In fact, according to an analysis carried out in the present paper, the proposed method is unconditionally stable. Numerical experiments are presented showing that the proposed approaches are extremely accurate and fast.
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中文摘要：
金融期权模型的最新更新是收益率跳跃的随机波动率模型下的美式期权（SVJ）和收益率和波动率跳跃的随机波动率模型（SVCJ）。为了评估这些选项，许多论文都采用了基于网格的方法，但众所周知，这些方法强烈依赖于网格特性，这是它们的主要缺点。因此，我们建议使用无网格方法来解决上述期权模型，特别是在本工作中，我们选择并分析了其中一种方案，即基于Wendland紧支撑径向基函数（WCS RBF）的局部径向点插值（LRPI），该径向基函数具有C6、C4和C2平滑度。LRPI方法是无网格局部Petrov-Galerkin方法（MLPG）的一种特殊类型，与基于网格的方法相比，LRPI方法具有许多优点，但至少据我们所知，它从未应用于期权定价。这些格式是真正的无网格方法，因为无论是形状函数的构造，还是局部子域的集成，都不需要传统的非重叠连续网格。在这项工作中，美式期权是一个自由边界问题，利用理查森外推技术将其简化为一个具有固定边界的问题。然后，时间导数采用隐式-显式（IMEX）时间步格式，使我们能够平滑期权收益的不连续性。对该方法进行了稳定性分析。事实上，根据本文进行的分析，所提出的方法是无条件稳定的。数值实验表明，所提出的方法是非常准确和快速的。
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分类信息：

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：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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