英文标题：
《Chebyshev Reduced Basis Function applied to Option Valuation》
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作者：
Javier de Frutos, Victor Gaton
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最新提交年份：
2017
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英文摘要：
  We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. In the paper we consider, as an example, a GARCH model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. In particular the method is applied to the problem of model calibration. The method is easily generalizable to be used with other models or problems.
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中文摘要：
我们提出了一种依赖于大量变量的金融衍生品频繁定价的数值方法。该方法基于构造多项式基，通过分层正交化过程对问题的值函数进行插值，从而减少精确表示值函数所需的自由度。本文以一个依赖于八个参数的GARCH模型为例，说明利用该方法可以在很短的计算时间内对大量不同到期日、资产和参数值的合同进行估值。特别是将该方法应用于模型标定问题。该方法很容易推广应用于其他模型或问题。
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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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