英文标题：
《Pricing Two-asset Options under Exponential L\\\'evy Model Using a Finite
Element Method》
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作者：
Xun Li, Ping Lin, Xue-Cheng Tai and Jinghui Zhou
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最新提交年份：
2015
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英文摘要：
This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-based solution. Then we discuss the localization of the infinite domain problem to a finite domain and analyze its error. We tackle the localized problem by an explicit-implicit time-discretization of the PIDE, where the space-discretization is done through a standard continuous finite element method. Error estimates are given for the fully discretized localized problem where two assets are assumed to have uncorrelated jumps. Numerical experiments for the polynomial option and a few other two-asset options shed light on good performance of our proposed method.
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中文摘要：
本文提出了一种求解偏积分微分方程（PIDE）的有限元方法（FEM），对两种资产期权进行定价，其基础价格过程由指数Levy过程建模。我们在加权Sobolev空间中给出了一个变分公式，并建立了基于有限元的解的存在唯一性。然后讨论了无限域问题在有限域上的局部化问题，并对其误差进行了分析。我们通过PIDE的显式-隐式时间离散化处理局部问题，其中空间离散化通过标准的连续有限元方法完成。对于完全离散的局部问题，假设两个资产具有不相关的跳跃，给出了误差估计。对多项式期权和其他两种资产期权的数值实验表明，我们提出的方法具有良好的性能。
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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：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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