英文标题：
《Low-rank tensor approximation for Chebyshev interpolation in parametric
  option pricing》
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作者：
Kathrin Glau, Daniel Kressner, Francesco Statti
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最新提交年份：
2019
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英文摘要：
  Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. Among the growing literature addressing this problem, Gass et al. [14] propose a complexity reduction technique for parametric option pricing based on Chebyshev interpolation. As the number of parameters increases, however, this method is affected by the curse of dimensionality. In this article, we extend this approach to treat high-dimensional problems: Additionally exploiting low-rank structures allows us to consider parameter spaces of high dimensions. The core of our method is to express the tensorized interpolation in tensor train (TT) format and to develop an efficient way, based on tensor completion, to approximate the interpolation coefficients. We apply the new method to two model problems: American option pricing in the Heston model and European basket option pricing in the multi-dimensional Black-Scholes model. In these examples we treat parameter spaces of dimensions up to 25. The numerical results confirm the low-rank structure of these problems and the effectiveness of our method compared to advanced techniques.
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中文摘要：
处理高维问题是开发用于解决金融问题的计算方法的主要挑战之一，在金融领域，定价、校准和风险评估等任务需要准确实时地执行。在不断增长的解决这一问题的文献中，Gass等人[14]提出了一种基于切比雪夫插值的参数期权定价复杂性降低技术。然而，随着参数数量的增加，这种方法会受到维数灾难的影响。在本文中，我们将此方法扩展到处理高维问题：此外，利用低秩结构可以考虑高维参数空间。该方法的核心是用张量序列（TT）格式表示张量化插值，并开发一种基于张量补全的有效方法来逼近插值系数。我们将新方法应用于两个模型问题：赫斯顿模型中的美式期权定价和多维Black-Scholes模型中的欧洲篮子期权定价。在这些示例中，我们处理维数高达25的参数空间。数值结果证实了这些问题的低阶结构以及我们的方法与先进技术相比的有效性。
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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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