英文标题：
《Magic points in finance: Empirical integration for parametric option
pricing》
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作者：
Maximilian Ga{\\ss}, Kathrin Glau, Maximilian Mair
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最新提交年份：
2016
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英文摘要：
We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpolation method of Barrault, Nguyen, Maday and Patera (2004) to parametric Fourier pricing. In the offline phase, a quadrature rule is tailored to the family of integrands of the parametric pricing problem. In the online phase, the quadrature rule then yields fast and accurate approximations of the option prices. Under analyticity assumptions the pricing error decays exponentially. Numerical experiments in one dimension confirm our theoretical findings and show a significant gain in efficiency, even for examples beyond the scope of the theoretical results.
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中文摘要：
我们提出了一种离线在线的基于傅立叶变换的期权定价方法。该方法支持加速数学金融的基本任务，如模型校准、实时定价，以及更普遍的风险评估和参数风险估计。我们将Barrault、Nguyen、Maday和Patera（2004）的经验幻点插值方法应用于参数傅里叶定价。在离线阶段，为参数定价问题的被积函数族定制一个求积规则。在在线阶段，求积规则会产生快速而准确的期权价格近似值。在分析性假设下，定价误差呈指数衰减。一维数值实验证实了我们的理论发现，并显示了效率的显著提高，即使是超出理论结果范围的例子。
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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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