英文标题：
《Model reduction for calibration of American options》
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作者：
Olena Burkovska, Kathrin Glau, Mirco Mahlstedt, Barbara Wohlmuth
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最新提交年份：
2016
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英文摘要：
American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European options, the mathematical model involves additional constraints, and a variational inequality is obtained. We use the Heston stochastic volatility model to describe the price of a single stock option. In order to speed up the calibration process, we apply two model reduction strategies. Firstly, a reduced basis method (RBM) is used to define a suitable low-dimensional basis for the numerical approximation of the parameter-dependent partial differential equation ($\\mu$PDE) model. By doing so the computational complexity for solving the $\\mu$PDE is drastically reduced, and applications of standard minimization algorithms for the calibration are significantly faster than working with a high-dimensional finite element basis. Secondly, so-called de-Americanization strategies are applied. Here, the main idea is to reformulate the calibration problem for American options as a problem for European options and to exploit closed-form solutions. Both reduction techniques are systematically compared and tested for both synthetic and market data sets.
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中文摘要：
美国看跌期权是交易最频繁的单一股票期权之一，由于没有可用的封闭式表达式，因此其校准在计算上具有挑战性。由于与欧式期权相比具有更高的灵活性，该数学模型包含了额外的约束，并得到了一个变分不等式。我们使用赫斯顿随机波动率模型来描述单个股票期权的价格。为了加快校准过程，我们采用了两种模型简化策略。首先，使用约化基方法（RBM）定义一个合适的低维基，用于参数相关偏微分方程（PDE）模型的数值逼近。通过这样做，解决$\\ mu$偏微分方程的计算复杂度大大降低，用于校准的标准最小化算法的应用速度明显快于使用高维有限元基矗其次，采用了所谓的非美国化策略。这里的主要思想是将美式期权的校准问题重新表述为欧式期权的问题，并利用闭式解。针对合成数据集和市场数据集，对这两种还原技术进行了系统的比较和测试。
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分类信息：

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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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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