英文标题：
《Chebyshev Interpolation for Parametric Option Pricing》
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作者：
Maximilian Ga{\\ss}, Kathrin Glau, Mirco Mahlstedt, Maximilian Mair
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最新提交年份：
2016
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英文摘要：
Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk management on the other. To address the resulting computational challenges, it is natural to exploit the recurrent nature of these tasks. We concentrate on Parametric Option Pricing (POP) and show that polynomial interpolation in the parameter space promises to reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify criteria for (sub)exponential convergence and explicit error bounds. We show that these results apply to a variety of European (basket) options and affine asset models. Numerical experiments confirm our findings. Exploring the potential of the method further, we empirically investigate the efficiency of the Chebyshev method for multivariate and path-dependent options.
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中文摘要：
定价、校准和风险评估等经常性任务需要准确、实时地执行。同时，我们观察到，一方面，模型复杂度有所提高，另一方面，对风险管理质量的要求也越来越高。为了解决由此带来的计算挑战，自然要利用这些任务的重复性。我们专注于参数期权定价（POP），并证明参数空间中的多项式插值可以在保持精度的同时减少运行时间。切比雪夫插值及其张量化扩展的吸引人的性质使我们能够确定（次）指数收敛的标准和显式误差界。我们证明了这些结果适用于各种欧洲（篮子）期权和仿射资产模型。数值实验证实了我们的发现。为了进一步探索该方法的潜力，我们实证研究了切比雪夫方法对多变量和路径依赖期权的有效性。
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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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